Use the normal distribution of fish lengths for which the mean is 11 inches and

Question

Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 4 inches. Assume the variable x is normally distributed. (a) What percent of the fish are longer than 12 inches? (b) If 400 fish are randomly selected, about how many would you expect to be shorter than 8 inches
Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 4 inches. Assume the variable x is normally distributed. (a) What percent of the fish are longer than 12 inches? (b) If 400 fish are randomly selected, about how many would you expect to be shorter than 8 inches
Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 4 inches. Assume the variable x is normally distributed. (a) What percent of the fish are longer than 12 inches? (b) If 400 fish are randomly selected, about how many would you expect to be shorter than 8 inches

Explanation / Answer

Params of normal distribution are given:

a. Mean = 11

Stdev = 4

a. P(X>12) = ?

P(Z> 12-11/4) = P(Z>.25) = 0,5987

b. P(Z<8) = ?

P(Z< 8-11/4 ) = P(Z< -.75) = .2266

So, if 400 fish are randomly selected, 400*.2266 =90.64 or 91 were expected to be shorter than 8 inches

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