STAT177 Homework sheet #2 Solutions

1) We choose binomial from the probability distributions menu on Gerry’s stats tools. The number of trials is 20, the number of successes is 1, the probability of success is 0.05, and the radio button is less than or equal to. The dialogue box gives the answer 73.58%.

2) The number of trials is 20, the number of successes is 2, the probability of success is 0.05, and the radio button is greater than or equal to. The dialogue box gives the answer 26.42%.

3) We have n = 20 x 5 = 100. Then m = 100(0.05) = 5.

4) We need m + 3s; m = 5000(0.05) = 250 and s = sqrt(250(0.95)) = 15.4. Then m + 3s = 250 + 3(15.4) = 296.2 which we round to 296.

5) A rate of 2.5 surveys/hour = 15 surveys/6 hours. We choose Poisson from the probability distributions menu. The value of x is 16, the mean is 15, and the radio button is greater than or equal to. The dialogue box gives the answer 43.19%.

6) The mean is 10 x 6 x 2.5 = 150. The value of x is 125, the mean is 150, and the radio button is greater than or equal to. The dialogue box gives the answer 98.35%.

7) We should expect 10 x 5 x 6 x 2.5 = 750 surveys to be completed.

8) A rate of 2.5 surveys per hour translates into 60/2.5 = 24 minutes between surveys. We choose exponential from the probability distributions menu. The value of x is 30, the mean is 24, and the radio button is greater than. The dialogue box gives the answer 28.65%.

9) The value of x is 15, the mean is 24, and the radio button is less than. The dialogue box gives the answer 46.47%.

10) The value of x is 2, the mean is 5, and the radio button is less than. The dialogue box gives the answer 32.97%.

11) The value of x is 15 – 5 = 10, the mean is 5, and the radio button is more than. The dialogue box gives the answer 13.53%.