### MAT 157 Q6b

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Q6b

1. Suppose that replacement times for washing machines have a mean of 9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected washing machines will have a mean replacement time less than 9.1 years.

2. Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective.

3. The amount of snowfall falling in a certain mountain range of the Rocky Mountains has a mean of 105 inches and a standard deviation of 16 inches. What is the probability that the mean annual snowfall during 64 randomly picked years will exceed 107.8 inches?

4. The weights of the fish in Lake Robbins have a mean of 14 lb. and a standard deviation of 6 lb. If 35 are randomly selected, what is the probability that their mean weight will be between 11.6 and 15.8 lb?

5. A typical question found on psychology exams is answered by only by 22% of the respondents. Everyone else just leaves it blank. Estimate the probability that among the next 150 responses there will be at most 40 that answer it correctly. Incidentally, the question is "Why?". Bet you don't know the answer.....

6. Compact Disks are manufactured in batches of 120 and the overall rate of defects is 5%. Estimate the probability that a randomly selected batch contains more than 6 defects.

7. A final exam in MATH 121 has a mean of 73 with a standard deviation 7.80. If 34 students are randomly selected, find the probability that the mean of their test scores is less than 76.

8. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1,050 kWh and a standard deviation of 218 kWh. If 50 different homes are randomly selected, find the probability that their mean energy consumption level for September would be between 1065 and 1095 kWh.

9. A "weird" coin has the probability of getting a tail on a single toss of .60. If the coin is tossed 22 times, would this be suitable to use the normal distribution as an approximation to finding probabilities?

10. A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct.

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