1. The time it takes me to wash the dishes is uniformly distributed between 12 minutes and 17 minutes. What is the probability that washing dishes tonight will take me between 13 and 16 minutes?

2. The probability density of a random variable X is given in the figure below.

From this density, the probability that X is between 0.02 and 1.08 is

3. The probability density of a random variable X is given in the figure below.

From this density, the probability that X is at least 1.56 is:

4. The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is more than 50.9 min. P(X > 50.9) = 5. The scores on a standardized test are normally distributed with a mean of 85 and standard deviation of 10. What test score is 1.3 standard deviations above the mean?

6. A normal distribution has a mean of 143 and a standard deviation of 4. Find the z-score for a data value of 139. Round to two decimal places

7. The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.6 inches and a standard deviation of 2.53 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? z = b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z = c) Who is relatively taller?

• The 5 foot 11 inch American woman
• The 6 foot 3 inch American man

8. For a standard normal distribution, find: P(z < -1.63) Express the probability as a decimal rounded to 4 decimal places.

9. For a standard normal distribution, find: P(-2.08 < z < 1.44)

10. For a standard normal distribution, find: P(z > c) = 0.8006 Find c rounded to two decimal places.

11. Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0C and a standard deviation of 1.00C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than -2.335C. P(Z<2.335)=

12. About __________ % of the area under the curve of the standard normal distribution is between z=1.342 and z=1.342 (or within 1.342 standard deviations of the mean).

13. About __________ % of the area under the curve of the standard normal distribution is outside the interval z=[-1.62,1.62] (or beyond 1.62 standard deviations of the mean).

14. A distribution of values is normal with a mean of 50.3 and a standard deviation of 55.7. Find the probability that a randomly selected value is less than 100.4. P(X < 100.4) = Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

15. A population of values has a normal distribution with =89.6 and =27.6. You intend to draw a random sample of size n=226. Find the probability that a sample of size n=226 is randomly selected with a mean between 86.5 and 92.7. P(86.5 < M < 92.7) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

16. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 250.4-cm and a standard deviation of 1.4-cm. For shipment, 22 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is greater than 250-cm. P(M > 250-cm) = Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

17. Assume that a sample is used to estimate a population proportion p. Find the margin of error M.E. that corresponds to a sample of size 293 with 25.9% successes at a confidence level of 98%. M.E. = ________ % Report answer accurate to one decimal place (as a number of percentage points). Answer should be obtained without any preliminary rounding (however, the critical value may be rounded to 3 decimal places).

18. We wish to estimate what percent of adult residents in a certain county are parents. Out of 100 adult residents sampled, 10 had kids. Based on this, construct a 95% confidence interval for the proportion of adult residents who are parents in this county. Give your answers as decimals, to three places. _________< < ___________

19. Assume that a sample is used to estimate a population mean . Find the margin of error M.E. that corresponds to a sample of size 8 with a mean of 26.1 and a standard deviation of 7.7 at a confidence level of 99.5%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = __________ Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

20. Assume that a sample is used to estimate a population mean . Find the 95% confidence interval for a sample of size 59 with a mean of 44.8 and a standard deviation of 17.4. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). 95% C.I. = ___________ Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

21. You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:

36.5

42.5

20.2

22.9

28.7

52.6

29.8

-5.5

Find the 90% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 90% C.I. = ____________