Question

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. d.) Would it be unusual if the sample mean were greater than 520? Round to at least four decimal places. 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. Please show how to input numbers in a TI-84 calculator.

Answer 1

d)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	495
std deviation   =σ=	111.0000
sample size       =n=	61
std error=σx̅=σ/√n=	14.2121

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

e)

since probability of above event is less than 0.05 , this should be considered unusual,

(for Ti-84 : press 2nd -vars -2:normalcdf -lower:520 , upper :1000000,mu:495 , sigma: 111/√(61) ,paste which will given u result 0.0393)