Question

Please do all three questions

1. Find P (0.2 < Z < 1.63) where Z is the standard normal variable.

2. Find x such that P(X > x) = 0.2 where X is normally distributed with mean 1 and standard deviation 2.6

3. The distribution of heights of adult males is normally distributed with mean 65 inches and standard deviation 2.3 inches. Answer the following.

(a) What minimum height is taller than 70% of all adult males?

(b) What two heights that are symmetric about the mean enclose the middle 82% of all heights?

Answer 1

1)

probability =

P(0.2<X<1.63)

=

P(0.2<Z<1.63)=

0.9484-0.5793=

0.3691

2)

mean μ=	1
standard deviation σ=	2.6000

for top 0.20 values fall at 80th percentile:

for 80th percentile critical value of z=		0.84
therefore corresponding value=mean+z*std deviation=			3.18

3)a)

70% tall people will fall at 30 th percentile:

for 30th percentile critical value of z=		-0.52
therefore corresponding value=mean+z*std deviation=			63.80

b) for middle 82% values ; critical z =1.34

therefore middle 82% values =65 -/+ 1.34 *2.3 =61.92 to 68.08