# 0.2 Practice tests (1-4) and final exams  (Page 35/36)

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12 . If a normally distributed random variable has µ = 0 and σ = 1, then 97.5% of the population values lie above:

1. –1.96.
2. 1.96.
3. 1.
4. –1.

Use the following information to answer the next three exercises. The amount of money a customer spends in one trip to the supermarket is known to have an exponential distribution. Suppose the average amount of money a customer spends in one trip to the supermarket is $72. 13 . What is the probability that one customer spends less than$72 in one trip to the supermarket?

1. 0.6321
2. 0.5000
3. 0.3714
4. 1

14 . How much money altogether would you expect the next five customers to spend in one trip to the supermarket (in dollars)?

1. 72
2. $\frac{{72}^{2}}{5}$
3. 5184
4. 360

15 . If you want to find the probability that the mean amount of money 50 customers spend in one trip to the supermarket is less than $60, the distribution to use is: 1. N (72, 72) 2. $N\left(72,\frac{72}{\sqrt{50}}\right)$ 3. Exp (72) 4. $Exp\left(\frac{1}{72}\right)$ Use the following information to answer the next three exercises: The amount of time it takes a fourth grader to carry out the trash is uniformly distributed in the interval from one to ten minutes. 16 . What is the probability that a randomly chosen fourth grader takes more than seven minutes to take out the trash? 1. $\frac{3}{9}$ 2. $\frac{7}{9}$ 3. $\frac{3}{10}$ 4. $\frac{7}{10}$ 17 . Which graph best shows the probability that a randomly chosen fourth grader takes more than six minutes to take out the trash given that he or she has already taken more than three minutes? 18 . We should expect a fourth grader to take how many minutes to take out the trash? 1. 4.5 2. 5.5 3. 5 4. 10 Use the following information to answer the next three exercises: At the beginning of the quarter, the amount of time a student waits in line at the campus cafeteria is normally distributed with a mean of five minutes and a standard deviation of 1.5 minutes. 19 . What is the 90 th percentile of waiting times (in minutes)? 1. 1.28 2. 90 3. 7.47 4. 6.92 20 . The median waiting time (in minutes) for one student is: 1. 5. 2. 50. 3. 2.5. 4. 1.5. 21 . Find the probability that the average wait time for ten students is at most 5.5 minutes. 1. 0.6301 2. 0.8541 3. 0.3694 4. 0.1459 22 . A sample of 80 software engineers in Silicon Valley is taken and it is found that 20% of them earn approximately$50,000 per year. A point estimate for the true proportion of engineers in Silicon Valley who earn \$50,000 per year is:

1. 16.
2. 0.2.
3. 1.
4. 0.95.

23 . If P ( Z < z α ) = 0.1587 where Z ~ N (0, 1), then α is equal to:

1. –1.
2. 0.1587.
3. 0.8413.
4. 1.

24 . A professor tested 35 students to determine their entering skills. At the end of the term, after completing the course, the same test was administered to the same 35 students to study their improvement. This would be a test of:

1. independent groups.
2. two proportions.
3. matched pairs, dependent groups.
4. exclusive groups.

A math exam was given to all the third grade children attending ABC School. Two random samples of scores were taken.

n $\overline{x}$ s
Boys 55 82 5
Girls 60 86 7

25 . Which of the following correctly describes the results of a hypothesis test of the claim, “There is a difference between the mean scores obtained by third grade girls and boys at the 5% level of significance”?

1. Do not reject H 0 . There is insufficient evidence to conclude that there is a difference in the mean scores.
2. Do not reject H 0 . There is sufficient evidence to conclude that there is a difference in the mean scores.
3. Reject H 0 . There is insufficient evidence to conclude that there is no difference in the mean scores.
4. Reject H 0 . There is sufficient evidence to conclude that there is a difference in the mean scores.

If a random variable X takes only two values -2 and 1 such that 2 P[X=- 2]=P[X=1]=P, then find variance of x.
2.5
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