Question

The blood cholesterol level of adult men has mean 188 mg/dl and standard deviation 41 mg/dl. Sketch the sampling distribution of x bar and calculate the probability that the sample mean will be greater than 193 mg/dl.

Answer 1

The probability that the sample mean will be greater than 193 mg/dl is 0.4522.

z score

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

$z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation$

Given that:

• μ = 188 mg/dl, σ = 41 mg/dl

For x > 193 mg/dl:

• $z=\frac{193-188}{41} =0.12$

P(x > 193) = P(z > 0.12) = 1 - P(z < 0.12) = 1 - 0.5478 = 0.4522

The probability that the sample mean will be greater than 193 mg/dl is 0.4522.

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