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STAT 108- 03 Exam III ID__________________________ _Name___________________________________

1) Assume that the weight loss for the first month of a diet program varies between 6 pounds

and 12 pounds, and is spread evenly over the range of possibilities, so that there is a

uniform distribution. Find the probability that pounds lost is between 7 pounds and 10

pounds

1)

For problem 2~ 5, assume that Z is a standard normal variable.

2) Find P(- 0.73 < Z < 2.27) 2)

3) Find the probability that Z is greater than - 1.82 3)

4) Find the percentage of data that are more than 1 standard deviation away from the mean. 4)

5) If P(Z > c) = 0.1093, find c. 5)

6) Assume that X has a normal distribution with the mean µ = 22.0 and the standarddeviation = 2.4. Find the probability that X is between 19.7 and 25.3 .

6)

7) Scores on a test are normally distributed with a mean of 65.3 and a standard deviation of

10.3. Find the score which separates the bottom 81% from the top 19%.

7)

8) The lengths of human pregnancies are normally distributed with a mean of 268 days and

a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300

days?

8)

9) A final exam in STAT 100 has a mean of 73 with standard deviation 8. If 25 students are

randomly selected, find the probability that the mean of their test scores is greater than 70

 but less than 78.

9)

10) The amount of snowfall falling in a certain mountain range is normally distributed with a

mean of 74 inches, and a standard deviation of 12 inches.

(a) What is the probability that the annual snowfall for a randomly picked year is lower

than 65 inches.

(b) What is the probability that the mean annual snowfall during 36 randomly picked

years will exceed 76.8 inches?

10)

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11) For the binomial distribution with n = 20 and p = 0.60, we want to estimate P(X < 8).

(a) Check the requirements for Normal Approximation.

(b) Using the continuity correction rewrite the probability statement.

(c) Using the Normal Approximation, estimate the probability.

11)

12) A product is manufactured in batches of 150 and the overall rate of defects is 10%.

(a) Find the mean and the standard deviation of the number of defects.

(b) Estimate the probability that a randomly selected batch contains more than 12 defects

using normal approximation.(don't forget the cotinuity correction)

12)

13) Find the critical value z/2 that corresponds to a degree of confidence of 92%. 13)

14)

^

The following confidence interval is obtained for a population proportion, p:

0.802 < p < 0.828

Use these confidence interval limits to find the point estimate, p and the margin error E.

14)

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

15) n = 102, x = 52; 88 percent 15)

16) When 306 college students are randomly selected and surveyed, it is found that 115 own a

car.

(a) Find the point estimate of the proportion of students who own a car.

(b) Find a 95% confidence interval for the true proportion of all college students who own a

car.

16)

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