Question

In: Statistics and Probability

If the distribution of the weights of all people traveling by air between Dallas and El...

If the distribution of the weights of all people traveling by air between Dallas and El Paso is normal with μ = 163 pounds, and σ = 18 pounds, then

(a) What’s the distribution of the sample mean of the weight of 36 passengers? Be specific and provide the mean and variance.

(b) What is the probability that the sample mean of the weight of 36 passengers exceeds 170 pounds?

Expert Solution

Given that, mean (μ) = 163 pounds and

standard deviation = 18 pounds

a) sample size (n) = 36

Since, sample size is large with known standard deviation, the sampling distribution of the sample mean is approximately normal.

Mean and variance of the sampling distribution of the sample mean are as follows :

=> Mean = 163 and Variance = 9

=> standard deviation = 3

b) We want to find,

Therefore, required probability is 0.0099

orchestra answered 2 years ago

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