Sample Means and Proportions Scavenger Hunt Review AP Statistics Sample Means and Proportions Scavenger Hunt Review

Directions Print slides and mount on the walls in your room, but in a random order. Assign students to start on a different problem. Answer to previous problem is at top of the next slide.

0.0423 Suppose that 47% of all adult women think they do not get enough time for themselves. An opinion poll interview 1025 women and records the sample proportion. Describe the distribution and find the mean and standard deviation of the sample.

Approx Normal; mean = 0.47, std dev = 0.016 The mean monthly fee that households pay service providers for Internet access is $28 with a standard deviation of $10, but the distribution is not normal. A sample survey asks a SRS of 500 households with Internet access how much they pay. What is the probability that the average fee paid by the sample households exceeds $29?

0.0126 A mail order company advertises that it ships 90% of its orders within 3 working days. You select a SRS size 100 of the 500 orders received in the past week for an audit. The audit shows 86 of these orders were shipped on time. What is the probability that 86 or fewer in a SRS of 100 are shipped on time?

0.0912 The average age of cars owned by residents of a small city is 4 years with a standard deviation of 2.2 years. A SRS of 400 cars is selected, and the sample mean age computed. Describe the distribution, the mean and standard deviation of the sample mean.

Approx normal with mean = 4, std dev = 0.11 A SRS of 100 Americans found that 61% were satisfied with service provided by the dealer from which they bought their car. Describe the distribution, mean, and standard deviation of the sample.

Approx normal with mean = 0.61, std dev = 0.049 The incomes in a certain large population of college teachers have a normal distribution with mean $35,000 and standard deviation $5000. Four teachers are selected at random from this population to serve on a salary review committee. What is the probability that their average salary exceeds $40,000?

0.0228 The strength of paper coming from a manufacturing plant is known to be 25 pounds/square inch with a standard deviation of 2.3. In a random sample of 40 pieces of paper, what is the probability that the mean strength is between 24.5 and 25.5 pounds/square inch?

0.8351 A promoter knows that 23% of males enjoy watching boxing matches. In a random sample of 125 men, what is the distribution, mean and standard deviation of the sample?

Approx normal with mean = 0.23, std dev = 0.38 A promoter knows that only 12% of females enjoy watching boxing matches. In a random sample of 125 women, what is the probability that more than 10% of the females enjoy watching boxing matches?

0.7548 The average number of missed school days for students in public schools is 8.5 with a standard deviation of 4.1. In a sample of 200 public school students, what is the probability that the average number of days missed is less than 8 days?

Answers Adult women & time for themselves: Internet access fees Approx normal, μ= .47, σ = .016 Np = 1025*.47 = 481.75 Nq = 1025 *.53 = 543.25 Internet access fees Approx normal with μ= 28, σ = 0.447 P(x-bar > 29) = 0.0126

Answers Mail order company Age of cars Approx normal with μ= .9, σ = .03 Np = .9 * 100 = 90, nq = .1 * 100 = 10 P(p-hat ≤ .86) = 0.0912 Age of cars Approx normal, mean = 4, std dev = 0.11

Answers Car Dealership service College teacher incomes Approx normal with mean = 0.61, std dev = 0.049 Np = 61, nq = 39 College teacher incomes P(x-bar ≥ 40,000) = 0.228 with std dev = 2500

Answers Paper strength Males & boxing matches Std dev = .36 P(24.5 ≤ x – bar ≤ 25.5) = .8351 Males & boxing matches Approx normal with mean = .23, std dev = 0.38 Np = .23 * 125 = 28.75 Nq = .77 * 125 = 96.25

Answers Females & boxing matches Missed school days Approx normal with mean = .12, std dev = .029 Np = 125 * .12 = 15 Nq = 125 *.88 = 110 P(p=hat ≥ 0.1) = .7548 Missed school days Std dev = .29 P(x-bar < 8) = .0423