Question

The mass of a species of mouse commonly found in houses is normally distributed with a mean of 19.8 grams with a standard deviation of 0.2 grams.

For parts (a) through (c), enter your responses as a decimal with 4 decimal places.

a) What is the probability that a randomly chosen mouse has a mass of less than 19.55 grams?

b) What is the probability that a randomly chosen mouse has a mass of more than 19.98 grams?

c) What proportion of mice have a mass between 19.64 and 19.96 grams?

d) 25% of all mice have a mass of less than grams.

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	19.8
std deviation   =σ=	0.2000

probability that a randomly chosen mouse has a mass of less than 19.55 grams:

probability =

P(X<19.55)

=

P(Z<-1.25)=

0.1056

b)

probability that a randomly chosen mouse has a mass of more than 19.98 grams:

probability =

P(X>19.98)

=

P(Z>0.9)=

1-P(Z<0.9)=

1-0.8159=

0.1841

c)proportion of mice have a mass between 19.64 and 19.96 grams:

probability =

P(19.64<X<19.96)

=

P(-0.8<Z<0.8)=

0.7881-0.2119=

0.5762

d)

for 25th percentile critical value of z=		-0.67
therefore corresponding value=mean+z*std deviation=			19.67 grams