Question

JKESTAT11 7.E.035.

MY NOTES

ASK YOUR TEACHER

Consider the approximately normal population of heights of male college students with mean μ = 67 inches and standard deviation of σ = 4.5 inches. A random sample of 13 heights is obtained.

(a) Describe the distribution of x, height of male college students.

skewed left

approximately normal

chi-square

skewed right

(b) Find the proportion of male college students whose height is greater than 71 inches. (Round your answer to four decimal places.)

  

(c) Describe the distribution of x, the mean of samples of size 13.

skewed right

approximately normal

chi-square

skewed left

(d) Find the mean of the x distribution. (Round your answer to the nearest whole number.)

  

(ii) Find the standard error of the x distribution. (Round your answer to two decimal places.)

  

(e) Find P(x > 72). (Round your answer to four decimal places.)

  

(f) Find P(x < 64). (Round your answer to four decimal places.)

Answer 1

a)

approximately normal

b)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	67
std deviation   =σ=	4.5000

probability =P(X>71)=P(Z>(71-67)/4.5)=P(Z>0.89)=1-P(Z<0.89)=1-0.8133=0.1867

c_)

approximately normal

d_)

mean of the x distribution =67

ii)

std error=σx̅=σ/√n=4.5/√13 =

1.25

e)

probability =P(X>72)=P(Z>(72-67)/1.25)=P(Z>4)=1-P(Z<4)=1-1=0.0000

f)

probability =P(X<64)=(Z<(64-67)/1.248)=P(Z<-2.4)=0.0082