Question

A manufacturer knows that their items have a normally distributed length, with a mean of 9.2 inches, and standard deviation of 2 inches. If 11 items are chosen at random, what is the probability that their mean length is less than 9.9 inches? round to 4 decimal places. & A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.2 years, and standard deviation of 2.4 years. If you randomly purchase 11 items, what is the probability that their mean life will be longer than 13 years? round to 4 decimal places

Answer 1

1)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	9.2
std deviation   =σ=	2.0000
sample size       =n=	11
std error=σx̅=σ/√n=	0.6030

probability that their mean length is less than 9.9 inches

probability =

P(X<9.9)

=

P(Z<1.16)=

0.8770

2)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	13.2
std deviation   =σ=	2.4000
sample size       =n=	11
std error=σx̅=σ/√n=	0.7236

probability that their mean life will be longer than 13 years :

probability =

P(X>13)

=

P(Z>-0.28)=

1-P(Z<-0.28)=

1-0.3897=

0.6103