The distribution of results from a cholesterol test has a mean of 180 and a stan

Question

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.
Find the probability that the sum of the 40 values is less than 7,050. (Round your answer to four decimal places.) The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.
Find the probability that the sum of the 40 values is less than 7,050. (Round your answer to four decimal places.) The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly.
Find the probability that the sum of the 40 values is less than 7,050. (Round your answer to four decimal places.)

Explanation / Answer

Let, X : sum of the 40 values
X follows Normal(180 x 40 , 20 x sqrt(40)) i.e. Normal(7200 , 126.49)
z = (X - 7200)/126.49
P(X < 7050) = P(z < -1.18) = 0.1178

probability that the sum of the 40 values is less than 7,050 is 0.1178

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