Question

Suppose the lengths of all fish in an area are normally distributed, with mean μ = 39 cm and standard deviation σ = 5 cm. What is the probability that a fish caught in an area will be between the following lengths? (Round your answers to four decimal places.)
(a) 39 and 44 cm long

(b) 33 and 39 cm long

Answer 1

Given,

= 39 , = 5

We convert this to standard normal as

P( X < x) = P (Z < x - / )

a)

P(39 < X < 44) = P( X < 44) - P( X < 39)

= P( Z < 44 - 39 / 5) - P( Z < 39 - 39 / 5)

= P( Z < 1) - P( Z < 0)

= 0.8413 - 0.50

= 0.3413

b)

P(33 < X < 39) = P( X < 39) - P( X < 33)

= P( Z < 39 - 39 / 5) - P( Z < 33 - 39 / 5)

= P( Z < 0) - P( Z < -1.2)

= 0.5 - 0.1151

= 0.3849