Question

15 #8

The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with μ=8.7 inches and σ=1.1inches.

(a) Find the probability that the length of a chosen fish was greater than 9.7 inches:  .

(b) Find the probability that the length of a chosen fish was between 7.7 and 9.7 inches:

Answer 1

Solution :

Given that

mean = = 8.7

standard deviation = = 1.1

(A)P(x >9.7 ) = 1 - P(x<9.7 )

= 1 - P[ X - / / (9.7-8.7) / 1.1]

= 1 - P(z <0.91 )

Using z table

= 1 -0.8186

= 0.1814

probability= 0.1814

(B)P(7.7< x < 9.7) = P[(7.7-8.7) /1.1 < (x - ) / < (9.7-8.7) /1.1)]

= P( -0.91< Z <0.91 )

= P(Z <0.91 ) - P(Z <-0.91 )

Using z table   

= 0.8186-0.1814

probability= 0.6372