Question

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11. Use the T1-84 Plus calculator. (a) Is it appropriate to use the normal distribution to find probabilities for x? (b) Find the probability that will be between 54 and 55. Round the answer to at least four decimal places (c) Find the 47th percentile of x. Round the answer to at least two decimal places. Yes (a) Is it appropriate to use the normal distribution to find probabilities for x? (b) The probability that x will be between 54 and 55 is c) The 47 percentile of x is !

Answer 1

a) Yes (as sample size is greater than 30)

b)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	53
std deviation   =σ=	11.000
sample size       =n=	45
std error=σx̅=σ/√n=	1.6398

probability =

P(54<X<55)

=

P(0.61<Z<1.22)=

0.8887-0.729=

0.1597

(use normalcdf function for ti-84)

c)

for 47th percentile critical value of z=		-0.075
therefore corresponding value=mean+z*std deviation=			52.88