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Question

Statistics homework help?
Your company is producing special battery packs for the most popular toy during the holiday season. The life span of the battery pack is known to be Normally distributed with a mean of 250 hours and a standard deviation of 20 hours.

1) What is the percentage of battery packs that last longer than 260 hours?
Give your answer to two decimal places.

2)If a simple random sample of four battery packs is selected from your company and we assume that their life spans are independent, the probability that they all last longer than 260 hours is ________.
Give your answer to 5 decimal places.

3)If a simple random sample of four battery packs is selected from your company, what is the probability that the average lifetime of these four packs is longer than 260 hours (express answer to 4 decimal places)?

Answer 1

1. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

2. Same, except to get probability that all events occur, multiply the probabilities of the individual events.

3. Since you are now dealing with the mean of the 4 packs, the equation becomes:

Z = (score-mean)/SEm

SEm = SD/√n

Use same table.

Answer 2

75%