Question

A sample of size 37 will be drawn from a population with mean 45 and standard deviation 9. Use the TI-84 Plus calculator.

(a) Is it appropriate to use the normal distribution to find probabilities for x?

(b) Find the probability that x will be between 46 and 47. Round the answer to at least four decimal places.

(c) Find the 39th percentile of x. Round the answer to at least two decimal places.

a)	Is it appropriate to use the normal distribution to find probabilities for x ?	Yes	No
(b)	The probability that x will be less than102 is.
(c)	The 95th percentile of x is.

Answer 1

a)Yes since the population is normal, therefore sampling distribution of mean will be normal for any sample size

b)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	45
std deviation   =σ=	9
sample size       =n=	37
std error=σx̅=σ/√n=	1.4796

probability =P(46<X<47)=P((46-45)/1.4796<Z<(47-45)/1.4796=P(0.68<Z<1.35)=0.9118-0.7504=0.1614

c)

for 39th percentile critical value of z=	-0.279
therefore corresponding value=mean+z*std deviation=	45.59