Question

SAT scores: Assume that in a given year the mean mathematics SAT score was 495, and the standard deviation was 111.
A sample of 61 scores is chosen. Use the TI-84 Plus calculator.

Part 1 of 5
(a) What is the probability that the sample mean score is less than 484? Round the answer to at least four
decimal places.
The probability that the sample mean score is less than 484 is?

Part 2 of 5
(b) What is the probability that the sample mean score is between 460 and 500? Round the answer to at least
four decimal places.
The probability that the sample mean score is between 460 and 500 is?

Part 3 of 5
(c) Find the 10th percentile of the sample mean. Round the answer to at least two decimal places.
The 10th percentile of the sample mean is?

Part 4 of 5
(d) Would it be unusual if the the sample mean were greater than 520? Round answer to at least four decimal places.
It (would/wouldnt) be unusual if the the sample mean were greater than 520, since the probability is?

Part 5 of 5
(e) Do you think it would be unusual for an individual to get a score greater than 520? Explain. Assume the
variable is normally distributed. Round the answer to at least four decimal places.
(yes/no) because the probabilities that an individual gets a score higher then 520 is?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	495
std deviation   =σ=	111.000
sample size       =n=	61
std error=σx̅=σ/√n=	14.21209

probability =P(X<484)=(Z<484-495)/14.212)=P(Z<(-0.774)=0.2195

b)

probability =P(460<X<500)=P((460-495)/14.212)<Z<(500-495)/14.212)=P(-2.46<Z<0.35)=0.6375-0.0069=0.6306

c)

for 10th percentile critical value of z=		-1.28
therefore corresponding value=mean+z*std deviation=			476.79

d)

probability =P(X>520)=P(Z>(520-495)/14.212)=P(Z>1.76)=1-P(Z<1.76)=1-0.9607=0.0393

It  would be unusual if the the sample mean were greater than 520, since the probability is 0.0393

e)

no  because the probabilities that an individual gets a score higher then 520 is 0.4109