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Answer :
A population of values has a normal distribution with μ = 167.4 and a = 97.7, a random sample of size n = 241, the probability that a sample of size n = 241 is randomly selected with a mean greater than 185.7.
P(M > 185.7) = 2.898.
To find the probability that a sample of size n = 241 has a mean greater than 185.7, we'll use the central limit theorem since the population follows a normal distribution.
Given:
- Population mean = 167.4
- Population standard deviation = 97.7
- Sample size = 241
- Sample mean = 185.7
First, we need to find the standard error of the sample mean (SE):
SE = 97.7 / √241
SE = 6.292
Now, let's calculate the z score:
z = (185.7 - 167.4) / (97.7 / √241)
z = 2.898.
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