CNNBC recently reported that the mean annual cost of auto insurance is 1038 dollars. Assume the standard deviation is 264 dollars. You take a simple random sample of 87 auto insurance policies. Find the probability that a single randomly selected value is less than 998 dollars. P(X < 998) = Find the probability that a sample of size n = 87 is randomly selected with a mean less than 998 dollars. P(M<998) =

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**Understanding Auto Insurance Costs**

CNNBC recently reported that the mean annual cost of auto insurance is 1038 dollars. Assume the standard deviation is 264 dollars. You take a simple random sample of 87 auto insurance policies.

**Question 1: Single Value Probability**
Find the probability that a single randomly selected value is less than 998 dollars.
\[ P(X < 998) = \]

**Question 2: Sample Mean Probability**
Find the probability that a sample of size \( n = 87 \) is randomly selected with a mean less than 998 dollars.
\[ P(M < 998) = \]

To solve these problems, we use the properties of the normal distribution.
Transcribed Image Text:**Understanding Auto Insurance Costs** CNNBC recently reported that the mean annual cost of auto insurance is 1038 dollars. Assume the standard deviation is 264 dollars. You take a simple random sample of 87 auto insurance policies. **Question 1: Single Value Probability** Find the probability that a single randomly selected value is less than 998 dollars. \[ P(X < 998) = \] **Question 2: Sample Mean Probability** Find the probability that a sample of size \( n = 87 \) is randomly selected with a mean less than 998 dollars. \[ P(M < 998) = \] To solve these problems, we use the properties of the normal distribution.
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