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. (A) What percent of the fish are longer than 14 ​inches? (B) If 300 fish are randomly​ selected, about how many would you expect to be shorter than 8 ​inches?

Answer 1

Explanation:

Given that fish length X is having the normal distribution for which the mean is 9 inches and the standard deviation is 2 inches.

X : N(9,2)

A)
`P(X<14) = P(z<(14-9)/(2) )\\=P(Z<2.5)\\=0.5+0.4938\\=0.9938`

B) Here sample size = 300

`P(X<8) = P(Z<(8-9)/(2) )=P(Z<-0.5)\\=0.3085`

Out of 300 fish we can expect 300(0.3085) to be shorter

i.e. 92.55=93 fish