AP Statistics - Chapter 5B Warm-Ups

11. / A simple random sample of 50 undergraduates at Johns Hopkins University found that 60% of those sampled felt that drinking was a problem among college students. A simple random sample of 50 undergraduates at Ohio State University found that 70% felt that drinking was a problem among college students. The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State is approximately 40,000. We conclude that
A) / the sample from Johns Hopkins has much less variability than that from Ohio State
B) / the sample from Johns Hopkins has much more variability than that from Ohio State
C) / the sample from Johns Hopkins has almost the same variability as that from Ohio State
D) / it is impossible to make any statements about the variability of the two samples since the students surveyed were different
23. / A random sample of size 25 is to be taken from a population that is normally distributed with mean 60 and standard deviation 10. The average J of the observations in our sample is to be computed. The sampling distribution of J is
A) / normal with mean 60 and standard deviation 10
B) / normal with mean 60 and standard deviation 2
C) / normal with mean 60 and standard deviation 0.4
D) / normal with mean 12 and standard deviation 2
25. / An automobile insurer has found that repair claims have a mean of $920 and a standard deviation of $870. Suppose that the next 100 claims can be regarded as a random sample from the long-run claims process. The mean and standard deviation of the average J of the next 100 claims is
A) / mean = $920 and standard deviation = $87
B) / mean = $920 and standard deviation = $8.70
C) / mean = $92 and standard deviation = $87
D) / mean = $92 and standard deviation = $870
32. / Suppose that you are a student worker in the statistics department and they agree to pay you using the Random Pay system. Each week the chair of the department flips a coin. If it comes up heads, your pay for the week is $80; if it comes up tails, your pay for the week is $40. Your friend is working for the engineering department and makes $65 per week. The probability that your total earnings in 100 weeks are more than hers is approximately
A) / 0.0000 B) 0.4013 C) 0.5000 D) 0.5987
34. / The weights of extra-large eggs have a normal distribution with a mean of 1 ounce and a standard deviation of 0.1 ounces. The probability that a dozen eggs weighs more than 13 ounces is closest to
A) / 0.0000 B) 0.0020 C) 0.1814 D) 0.2033

The SAT scores of entering freshmen at University X have a N(1200, 90) distribution, and the SAT scores of entering freshmen at University Y have a N(1215, 110) distribution. A random sample of 100 freshmen is sampled from each university, with J the sample mean of the 100 scores from University X and M the sample mean of the 100 scores from University Y.

38. / The probability that J is less than 1190 is
A) / 0.0116 B) 0.1335 C) 0.4090 D) 0.4562
39. / The probability that M less than 1190 is
A) / 0.0116 B) 0.1335 C) 0.4090 D) 0.4562

Answer Key

7. / D
8. / D
10. / A
11. / C
23. / B
25. / A
27. / B
32. / B
33. / B
34. / B
38. / B
39. / A

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