Use the normal distribution of fish lengths for which the mean is 9 inches and t

Question

Use the normal distribution of fish lengths for which the mean is 9 inches and the standard deviation is 2 inches. Assume the variable x is normally distributed. left parenthesis a right parenthesis What percent of the fish are longer than 12 inches? left parenthesis b right parenthesis If 200 fish are randomly selected, about how many would you expect to be shorter than 6 inches? left parenthesis a right parenthesis Approximately nothing% of fish are longer than 12 inches. (Round to two decimal places as needed.) left parenthesis b right parenthesis You would expect approximately nothing fish to be shorter than 6 inches. (Round to the nearest fish.)

Explanation / Answer

A) P(X > 12) = P((x - mean)/SD > (12 - mean)/SD)

= P(Z > (12 - 9)/2)

= P (Z > 1.5)

= 1 - P(Z < 1.5)

= 1 - 0.9332 = 0.0668

B) P(X < 6) = P(x - mean)/SD < (6 - mean)/SD)

= P(Z < (6 - 9)/2)

= P(Z < -1.5)

= 0.0668

No of fish shorter than 6inches = 0.0668 * 200 = 13.36

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