a. This is a GROUP assignment.
b. Each student must be a member of a group of 4 or 5 students, selected by lecturer. c. Solutions from each group must be submitted by 19 April 2013.

SPECIAL DISTRIBUTIONS

I. Concept of probability (3%)

1. Explain why the distribution B(n,p) can be approximated by Poisson distribution with parameter if n tends to infinity, p 0, and = np can be considered constant.

2. Show that – and + are the turning points in the graph of the p.d.f. of normal distribution with mean and standard deviation .

3. What is the relationship between exponential distribution and Poisson distribution?

II. Computation of probability (7%)

1. Let the random variable X follow a Binomial distribution with parameters n and p. We write X ~ B(n,p). * Write down all basic assumptions of Binomial distribution. * Knowing the p.m.f. of X, show that the mean and variance of X are = np, and 2 = np(1 – p), respectively.

2. A batch contains 40 bacteria cells and 12 of them are not capable of cellular replication. Suppose you examine 3 bacteria cells selected at random without replacement. What is the probability that at least one of the selected cells cannot replicate?

3. Redo problem No. 2 if the 3 bacteria cells are selected at random with replacement.

4. The number of customers who enter a bank in an hour follows a Poisson distribution. If P(X = 0) = 0.05, determine the mean and variance of the number of customers in an hour.

5. In a large corporate computer network, user log-ons to the system can be modeled as a Poisson process with a mean of 25 log-ons per hour. What is the probability that there are no log-ons in an interval of 6 minutes?

6. The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a...

...standard deviation = square root of variance = sqrt(846) = 29.086 4. If we have the following data
34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66 Draw a stem and leaf. Discuss the shape of the distribution. Solution: 2 3 4 5 6 | | | | | 219200 48714 0197 6
This distribution is right skewed (positively skewed) because the “tail” extends to the right. 5. What type of relationship is shown by this scatter plot?
45 40 35 30 25 20 15 10 5 0 0 5...

...What are the characteristics of a population for which a mean/median/mode would be appropriate? Inappropriate?
The analysis of data begins with descriptive statistics such as the mean, median, mode, range, 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...

...NORMALDISTRIBUTION
1. Find the
distribution:
a.
b.
c.
d.
e.
f.
following probabilities, the random variable Z has standard normal
P (0< Z < 1.43)
P (0.11 < Z < 1.98)
P (-0.39 < Z < 1.22)
P (Z < 0.92)
P (Z > -1.78)
P (Z < -2.08)
2. Determine the areas under the standard normal curve between –z and +z:
♦ z = 0.5
♦ z = 2.0
Find the two values of z in standard normaldistribution so that:
P(-z < Z...

...distributed with μ = 110 grams and σ = 25 grams. A sample of 25 vitamins is to be selected. So, 95% of all sample means will be greater than how many grams?
TABLE 7-1
Times spent studying by students in the week before final exams follow a normaldistribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students.
11)
Referring to Table 7-1, what is...

...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...

...Pages
C H A P T E
R
6
The NormalDistribution
Objectives
Outline
After completing this chapter, you should be able to
1
2
3
Identify distributions as symmetric or skewed.
4
Find probabilities for a normally distributed
variable by transforming it into a standard
normal variable.
Introduction
6–1
NormalDistributions
Identify the properties of a...

...
NormalDistributionNormaldistribution is a statistics, which have been widely applied of all mathematical concepts, among large number of statisticians. Abraham de Moivre, an 18th century statistician and consultant to gamblers, noticed that as the number of events (N) increased, the distribution approached, forming a very smooth curve.
He insisted that a new...

...School: Science, Technology, Engineering, and MathCourse Number: Math 302Course Name: StatisticsCredit Hours: 3 Credit HoursLength of Course: 16 WeeksPrerequisite: Math 110, College Algebra or an equivalent course |
Table of Contents |
Instructor Information | Evaluation Procedures |
Course Description | Evaluation Criteria |
Course Scope | Course Outline |
Course Objectives | Policies |
Course Delivery Method | Academic Services |
Course...

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