Question

Suppose height of individuals in a population is normally distributed with mean of 66 inches and a standard deviation of 4 inches. A sample of 9 individuals is taken from this population and their average height (i.e., Xˉ ) is computed.

Compute P( X <65)

−0.0122
0.7734
0.2266
0.9878
0.9082
0.5987
0.4013
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Answer 1

To compute the probability P(X < 65), we need to standardize the value 65 using the formula z = (X - μ) / σ. The probability P(X < 65) is approximately 0.4013.

Step-by-step explanation:

To compute the probability P(X < 65), we first need to standardize the value 65 using the formula z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (65 - 66) / 4 = -0.25. Now, we can use a standard normal distribution table or calculator to find the probability. The probability P(X < 65) is approximately 0.4013, which corresponds to option C.