Question

Traveling time between the mall and school is normally distributed, with a mean equal to 22 minutes and a variance of 23 minutes. Taking a random sample of 8 trips, the probability that the sample variance is higher than 13 is

the sample average is less than 24 mins

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	22
std deviation   =σ= √23 =	4.796
sample size       =n=	8
std error=σx̅=σ/√n=	1.6956

1)

  probability that the sample variance is higher than 13:

probability =P(X>13)=P(Z>(13-22)/1.696)=P(Z>-5.31)=1-P(Z<-5.31)=1-0.000=1.0000

2)

P(sample average is less than 24 mins):

probability =P(X<24)=(Z<(24-22)/1.696)=P(Z<1.18)=0.8810