CNNBC recently reported that the mean annual cost of auto insurance is 1032 dollars. Assume the standard deviation is 164 dollars. You will use a simple random sample of 78 auto insurance policies. Find the probability that a single randomly selected policy has a mean value between 996.7 and 1048.7 dollars. P(996.7 < X < 1048.7) = Find the probability that a random sample of size n = 78 has a mean value between 996.7 and 1048.7 dollars. P(996.7 M 1048.7) = Enter your answers as numbers accurate to 4 decimal places.

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CNNBC recently reported that the mean annual cost of auto insurance is 1032 dollars. Assume the standard deviation is 164 dollars. You will use a simple random sample of 78 auto insurance policies.

Find the probability that a single randomly selected policy has a mean value between 996.7 and 1048.7 dollars.

\[P(996.7 < X < 1048.7) = \text{______}\]

Find the probability that a random sample of size \( n = 78 \) has a mean value between 996.7 and 1048.7 dollars.

\[P(996.7 < M < 1048.7) = \text{______}\]

Enter your answers as numbers accurate to 4 decimal places.
Transcribed Image Text:CNNBC recently reported that the mean annual cost of auto insurance is 1032 dollars. Assume the standard deviation is 164 dollars. You will use a simple random sample of 78 auto insurance policies. Find the probability that a single randomly selected policy has a mean value between 996.7 and 1048.7 dollars. \[P(996.7 < X < 1048.7) = \text{______}\] Find the probability that a random sample of size \( n = 78 \) has a mean value between 996.7 and 1048.7 dollars. \[P(996.7 < M < 1048.7) = \text{______}\] Enter your answers as numbers accurate to 4 decimal places.
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