Use the normal distribution of fish lengths for which the mean is 8 inches and t

Question

Use the normal distribution of fish lengths for which the mean is 8 inches and the standard deviation is 5 inches Assume the variable x is normally distributed. (a) What percent of the fish are longer than 11 inches? (b) If 200 fish are randomly selected, about how many would you expect to be shorter than 7 inches? (a) Approximately 17% of fish are longer than 11 inches. S (Round to two decimal places as needed.) al (b) You would expect approximately fish to be shorter than 7 inches. Round to the nearest fish.)

Explanation / Answer

a) P(X > 11)

= P(z > (11 - 8)/5)

= P(z > 0.6)

= 0.2743

= 27.43%

b) P(X < 7)

= P(z < (7 - 8)/5)

= P(z < -0.2)

= 0.4207

So,

We would expect 0.4207(200) i.e. 84 fish to be shorter than 7 inches.

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