# Math 116

**Topics:**Normal distribution, Standard deviation, Binomial distribution

**Pages:**5 (1192 words)

**Published:**June 22, 2013

1)

Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike? 2)

Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning. 3)

Which of the variables below do you think will be roughly normally distributed?

a. Weights of 10 year old boys

b. Incomes of 40 year old adults

c. The numbers that show up when you roll a balanced die

d. The amount of coffee which a filling machine puts into "4 ounce jars" Fill in the blanks by standardizing the normally distributed variable. 4)

Dave drives to work each morning at about the same time. His commute time is normally distributed with a mean of 42 minutes and a standard deviation of 4 minutes. The percentage of time that his commute time lies between 50 and 54 minutes is equal to the area under the standard normal curve between ___ and ___. Use a table of areas to find the specified area under the standard normal curve. 5)

The area that lies between 0 and 3.01

6)

The area that lies between -1.10 and -0.36

Use a table of areas for the standard normal curve to find the required z-score. 7)

Find the z-score for having area 0.07 to its right under the standard normal curve, that is, find [pic]. 8)

Find the z-score for which the area under the standard normal curve to its left is 0.04 9)

Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas. Find the indicated probability or percentage for the normally distributed variable. 10)

The variable X is normally distributed. The mean is μ = 15.2 and the standard deviation is σ = 0.9. Find P(X > 16.1).

11)

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter smaller than 0.32 inches? 12)

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275. 13)

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure that lies within 3 standard deviations to either side of the mean?

Find the specified percentile, quartile, or decile.

14)

The annual precipitation for one city is normally distributed with a mean of 39.2 inches and a standard deviation of 2.6 inches. Find the 2nd decile. This is the same as the 20th percentile. 15)

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find the 6th decile. This is the same as the 60th percentile. Provide an appropriate response.

16)

True or false, areas under the standard normal curve cannot be negative, whereas z-scores can be positive or negative? 17)

Most problems involving normally distributed variables are one of two types.

Type A: Find a probability or percentage, e.g. find the probability that X lies in a specified range.

Type B: Find the observation corresponding to a given probability or percentage.

Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Which of the following questions below are of type B?

a. Find the 80th percentile.

b. Find the cutoff for the A grade if the top 10% get an A.

c. Find the percentage scoring more than 90.

d. Find the score that separates the...

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