A population value has a normal distribution with μ=245.4 and σ=76.4. A random sample of size n=231 is drawn. Find the probability that a single randomly selected value is between 238.4 and 251.4. Find the probability that a sample size of n=231 is randomly selected with a mean between 238.4 and 251.4

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A population value has a normal distribution with μ=245.4 and σ=76.4. A random sample of size n=231 is drawn. Find the probability that a single randomly selected value is between 238.4 and 251.4. Find the probability that a sample size of n=231 is randomly selected with a mean between 238.4 and 251.4.
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Statistics homework question answer, step 1, image 1

The probability that a single randomly selected value is between 238.4 and 251.4 can be calculated as:

Statistics homework question answer, step 1, image 2

By using the standard normal table,

Statistics homework question answer, step 1, image 3Statistics homework question answer, step 1, image 4

Hence, the probability that a single randomly selected value is between 238.4 and 251.4 is,

0.0678
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