Question

The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.8 grams with a standard deviation of 0.18 grams.

a) What is the probability that a randomly chosen mouse has a mass of less than 20.64 grams?

b) What is the probability that a randomly chosen mouse has a mass of more than 20.99 grams?

c) What proportion of mice have a mass between 20.71 and 20.9 grams?

Answer 1

Solution :

Given that ,

mean =   = 20.8

standard deviation = =0.18

P(X<20.64 ) = P[(X- ) / < (20.64 - 20.8) /0.18 ]

= P(z <-0.89 )

Using z table

=0.1867

b.

P(x >20.99 ) = 1 - P(x<20.99 )

= 1 - P[(x -) / < (20.99-20.8) /0.18 ]

= 1 - P(z <1.06 )

Using z table

= 1 - 0.8554

= 0.1446

probability= 0.1446

c.

P(20.71< x <20.9 ) = P[(20.71-20.8) /0.18 < (x - ) / < (20.9-20.8) /0.18]

= P( -0.5< Z <0.56 )

= P(Z < 0.56) - P(Z <-0.5 )

Using z table   

= 0.7123 - 0.3085

proportion= 0.4038