Question

1. Consider a normal distribution with mean 200 and standard deviation 20.

a) Find the proportion of the distribution with values between 190 and 220. Illustrate your calculation with a sketch.

b) Find the value of x such that the proportion of the distribution with values between 200-x and 200+x is 0.75. Illustrate your calculation with a sketch.

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	200
std deviation   =σ=	20.0000

proportion of the distribution with values between 190 and 220:

probability =

P(190<X<220)

=

P(-0.5<Z<1)=

0.8413-0.3085=

0.5328

b)

for middle 75% values critical z =1.15

hence values are =mean -/+z*std deviation =200-/+1.15*20 =177 and 223