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.