Question

4. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.4 years, and standard deviation of 3.2 years. If you randomly purchase 21 items, what is the probability that their mean life will be longer than 15 years? (Give answer to 4 decimal places.)

5. A particular fruit's weights are normally distributed, with a mean of 704 grams and a standard deviation of 12 grams. If you pick 12 fruit at random, what is the probability that their mean weight will be between 692 grams and 701 grams (Give answer to 4 decimal places.)

6. A particular fruit's weights are normally distributed, with a mean of 286 grams and a standard deviation of 18 grams. If you pick 25 fruit at random, what is the probability that their mean weight will be between 291 grams and 295 grams (Give answer to 4 decimal places.)

7. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.7 years, and standard deviation of 3.1 years. If 16 items are picked at random, 4% of the time their mean life will be less than how many years? Give your answer to one decimal place.

8. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13 years, and standard deviation of 3.5 years. If 2 items are picked at random, 7% of the time their mean life will be less than how many years? Give your answer to one decimal place.

9. A particular fruit's weights are normally distributed, with a mean of 658 grams and a standard deviation of 20 grams. If you pick 31 fruits at random, then 15% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

10. A particular fruit's weights are normally distributed, with a mean of 658 grams and a standard deviation of 18 grams. If you pick 23 fruits at random, then 17% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

Answer 1

Solution:

Question 4:

Given: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.4 years, and standard deviation of 3.2 years.

That is:

Sample size = n = 21

We have to find the probability that their mean life will be longer than 15 years.

that is:

Find z score:

Thus we get:

Look in z table for z = 0.8 and 0.06 and find area.

P(Z<0.86) = 0.8051

thus we get: