Ans : a) P( Z > 2.58) = 0.0049 ( 4 decimal places)
b) P ( Z < -1) = 0.1587 ( 4 decimal places)
c) P ( -1.5≦ Z < 5) = P ( -1.5 < Z < 5)
= (0.5- 0.0668) + ( 0.5 -0) = 0.9332 ( 4 decimal places)

2.Find the value of z if the area under a Standard Normal curve a)to the right of z is 0.3632;
b)to the left of z is 0.1131;
c)between 0 and z, with z > 0, is 0.4838;
d)between -z and z, with z > 0, is 0.9500.

Ans : a) z = + 0.35 ( find 0.5- 0.3632 = 0.1368 in the normal table) b) z = -1.21 ( find 0.5 – 0.1131 = 0.3869 in the normal table) c ) the area between 0 to z is 0.4838, z = 2.14
d) the area to the right of +z = ( 1-0.95)/2 = 0.025, therefore z = 1.96

3.Given the Normally distributed variable X with mean 18 and standard deviation 2.5, find a)P(X < 15);
b)the value of k such that P(X < k) = 0.2236;
c)the value of k such that P(X > k) = 0.1814;
d)P( 17 < X < 21).

Ans : X ~ N ( 18, 2.52)

a) P ( X < 15)
P ( Z < (15-18)/2.5) = P ( Z < -1.2) = 0.1151 ( 4 decimal places)

b) P ( X < k) = 0.2236
P ( Z < ( k – 18) / 2.5 ) = 0.2236
From normal table, 0.2236 = -0.76
(k-18)/2.5 = - 0.76, solve k = 16.1

c) P (X > k) = 0.1814
P ( Z > (k-18)/2.5 ) = 0.1814
From normal table, 0.1814 = 0.91
(k-18)/ 2.5 = 0.91, solve k = 20.275

d) P ( 17 < X < 21)
P ( (17 -18)/2.5 < Z < ( 21-18)/2.5)
P ( -0.4 < Z < 1.2) = 0.8849 – 0.3446 = 0.5403 ( 4 decimal places)

4.In a sample of 25 observations from a Normal Distribution with mean 98.6 and standard deviation 17.2, find:

Ans: a) n = 25, [pic] = ( = 98.6, [pic] = /n = 17.2/(25 = 3.44 [pic]( N...

... standard deviation, variance, standard error of the mean, and confidence intervals. These statistics are used to summarize data and provide information about the sample from which the data were drawn and the accuracy with which the sample represents the population of interest. The mean, median, and mode are measurements of the “central tendency” of the data. The range, standard deviation, variance, standard error of the mean, and confidence intervals provide information about the “dispersion” or variability of the data about the measurements of central tendency.
MEASUREMENTS OF CENTRAL TENDENCY The appropriateness of using the mean, median, or mode in data analysis is dependent upon the nature of the data set and its distribution (normal vs non-normal). The mean (denoted by x) is calculated by dividing the sum of the individual data points (where Σ equals “sum of”) by the number of observations (denoted by n). It is the arithmetic average of the observations and is used to describe the center of a data set.
mean=x= One of the most basic purposes of statistics is simply to enable us to make sense of large numbers. For example, if you want to know how the students in your school are doing in the statewide achievement test, and somebody gives you a list of all 600 of their scores, that’s useless. This everyday problem is even more obvious and staggering when you’re dealing, let’s say, with the population data for the nation....

...STATISTICS FOR MANAGEMENT
B1731
4
60
Note: Answer all questions. Kindly note that answers for 10 marks questions should be
approximately of 400 words. Each question is followed by evaluation scheme.
Questions
Marks
Total Marks
Q.No
1
Distinguish between Classification and Tabulation. Explain the structure and
components of a Table with an example.
Meaning of Classification and Tabulation
Differences between Classification and Tabulation
2
Structure and Components of a Table with an example
2
2
10
6
a) Describe the characteristics of Normal probability distribution.
b) In a sample of 120 workers in a factory, the mean and standard deviation of wages
were Rs. 11.35 and Rs.3.03 respectively. Find the percentage of workers getting wages
between Rs.9 and Rs.17 in the whole factory assuming that the wages are normally
distributed.
Characteristics of Normal probability distribution
Formula/Computation/Solution to the problem
3
4
10
6
a) The procedure of testing hypothesis requires a researcher to adopt several steps.
Describe in brief all such steps.
b) Distinguish between:
i. Stratified random sampling and Systematic sampling
ii. Judgement sampling and Convenience sampling
Hypothesis testing procedure
4
Differences
10
6
(3 each)
4
a) What is regression analysis? How does it differ from correlation analysis?
b) Calculate Karl Pearson’s...

...time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. a) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes. b) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes. c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. d) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes. ANSWER: c 2. Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? a) The mean of the sampling distribution is equal to 23 years. b) The standard deviation of the sampling distribution is equal to 3 years. c) The shape of the sampling distribution is approximately normal. d) The standard error of the sampling distribution is equal to 0.3 years. ANSWER: b 3....

...Probability and statistics - Karol Flisikowski
n
Sampling Distribution of x-bar
How does x-bar behave? To study the behavior,
imagine taking many random samples of size n, and computing an x-bar for each of the samples. Then we plot this set of x-bars with a histogram.
Probability and statistics - Karol Flisikowski
Sampling Distribution of x-bar
Probability and statistics - Karol Flisikowski
Central Limit Theorem
The key to the behavior of x-bar is the central limit
theorem. It says: Suppose the population has mean, m, and standard deviation s. Then, if the sample size, n, is large enough, the distribution of the sample mean, x-bar will have a normal shape, the center will be the mean of the original population, m, and the standard deviation of the x-bars will be s divided by the square root of n.
Probability and statistics - Karol Flisikowski
Central Limit Theorem
If the CLT holds we have,
Normal shape
Center = mu
Spread = sigma/sqroot n.
Probability and statistics - Karol Flisikowski
When Does CLT Hold?
Answer generally depends on the sample size, n,
and the shape of the original distribution. General Rule: the more skewed the population distribution of the data, the larger sample size is needed for the CLT to hold.
Probability and statistics - Karol Flisikowski
CLT
Previous overhead shows...

...Applied Statistics for Healthcare Professionals
Date: 04/01/2015
EXERCISE 18 • Mean, Standard Deviation, and 95% and 99% of the Normal Curve
1. Assuming that the distribution is normal for weight relative to the ideal and 99% of the male participants scored between (–53.68, 64.64), where did 95% of the values for weight relative to the ideal lie? Round your answer to two decimal places.
In order to find where 95% of the values for the weight of relative to the ideal lies you would use the formula that is presented in the text on page 132 of Exercise 18. This formula is:. The = MEAN (5.48) and the (SD) =Standard Deviation (22.93). These numbers were derived from table 1 on pg.133 under the column labeled Male. The problem is worked out as such:
Formula: 5.48±1.96(22.93)
5.48-1.96(22.93) = 5.48-44.94
5.48-44.94= -39.46
5.48+1.96(22.93) = 5.48+44.94
5.48+44.94= 50.42
ANSWER= (-39.46,50.42)
2. Which of the following values from Table 1 tells us about variability of the scores in a distribution?
a. 60.22
b. 11.94
c. 22.57 ←Answer
d. 53.66
The answer for question number 2 is (C). The SD indicates the variability. In the answer set the only choice that was SD was choice (C) the other options were Mean scores listed in table 1.
3. Assuming that the distribution for General Health Perceptions is normal, 95% of the females’ scores around...

...hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normaldistribution.
a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect?
z(29) = (29-32)/2 = -3/2
z(34) = (34-32)/2 = 1
z(32) = 0
P(32 < x < 34) = P(0< z < 1) = 0.34
b. What percent of the garages take between 29 hours and 34 hours to erect?
P(29 < x < 34) = P(-1.5 < z < 1) = 0.7745
c. What percent of the garages take 28.7 hours or less to erect?
z(28.7) = (28.7-32)/2 = -3.3
P(0 < x < 28.7) = P (-10 < z < -3.3) = 0.00048348...
d. Of the garages, 5 percent take how many hours or more to erect?
find the z-value corresponding to an area of 95% to the left and only
5% to the right under the curve.
Use your z-chart or InvNor(0.95) = 1.645 on your calculator.
Now find the x-value corresponding to that z-value.
1.645 = (x-32)/2
x-32 = 2*1.645
x= 35.29 hours
5% of the houses require 35.29 or more hours to erect.
Chapter 8 #21
What is a sampling error?
Sampling error is the expected chance difference, variation, or deviation between a random sample and the population.
Chapter 8 #34
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normaldistribution with a standard deviation of...

...
Student Exploration: Sight vs. Sound Reactions
Vocabulary: histogram, mean, normaldistribution, range, standard deviation, stimulus
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Most professional baseball pitchers can throw a fastball over 145 km/h (90 mph). This gives the batter less than half a second to read the pitch, decide whether to swing, and then try to hit the ball. No wonder hitting a baseball is considered one of the hardest things to do in sports!
1. What are some things in your life you must react to quickly? You need to react quickly when you are in danger, and you need to get away. You also need to react quickly when you are in a car so you don’t get hurt
2. In general, do you think you have quick, slow, or average reactions? I think I have relatively quick reactions, because when I am in a car, I can react to things very fast and when there are things that happy quickly, I can follow them.
Gizmo Warm-up
A stimulus is something that can cause you to react. A stimulus can be something you see (visual stimulus), something you hear (auditory stimulus), something you touch (tactile stimulus), or something you smell (olfactory stimulus). In the Sight vs. Sound Reactions Gizmo™, you will compare your reactions to visual and auditory stimuli.
To start, check that the Test is Sight. Click the Start button. When you see a red circle, immediately click your mouse. Take the test until the...

...standard deviation of the [pic] sampling distribution? Can we say that the shape of the distribution is approximately normal? Why or why not? (10 points)
(b) What is the probability that [pic] will be within 0.5 of the population mean? (5 points)
(c) What is the probability that [pic] will differ from the population mean by more than 0.7? (5 points)
4. In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. Furthermore, there is a weight limit of 2500 pounds. Assume that the average weight of students, faculty, and staff on campus is 150 pounds with a standard deviation of 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. If a random sample of 16 persons from the campus is taken:
(a) What is the mean and standard deviation of the [pic] = sample mean distribution? Can we assume the [pic] distribution is normal? Explain. (10 points)
(b) What average weights of for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 pounds? (5 points)
(c) What is the chance that a random sample of 16 persons on the elevator will exceed the weight limit? (5 points)
5. A random sample is to be selected from a population that has a proportion of...