Question

Assume that in a given year the mean mathematics SAT score was 467, and the standard deviation was 105. A sample of 59 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 455? Round the answer to at least four decimal places. The probability that the sample mean score is less than 455 is . Part 2 of 5 (b) What is the probability that the sample mean score is between 430 and 470? Round the answer to at least four decimal places. The probability that the sample mean score is between 430 and 470 is . Part 3 of 5 (c) Find the 45th percentile of the sample mean. Round the answer to at least two decimal places. The 45th percentile of the sample mean is . Part 4 of 5 (d) Would it be unusual if the the sample mean were greater than 499? Round answer to at least four decimal places. It ▼(Choose one) be unusual if the the sample mean were greater than 499, 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 499? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places. ▼(Choose one), because the probability that an individual gets a score greater than 499 is .

Answer 1

1)

mean μ=	467
standard deviation σ=	105.00
sample size       =n=	59
std error=σx̅=σ/√n=	13.6698

a)

probability =P(X<455)=(Z<455-467)/13.67)=P(Z<(-0.8778)=0.1900

if using ti-84 use command :normalcdf(60,75,467,13.6698)

b)

probability =P(430<X<470)=P((430-467)/13.67)<Z<(470-467)/13.67)=P(-2.71<Z<0.22)=0.5869-0.0034=0.5835

if using ti-84 use command :normalcdf(430,470,467,13.6698)

c)

for 45th percentile critical value of z=		-0.13
therefore corresponding value=mean+z*std deviation=			465.28

d)

probability =P(X>499)=P(Z>(499-467)/13.67)=P(Z>2.34)=1-P(Z<2.34)=1-0.9904=0.0096

it will be unusual if the the sample mean were greater than 499, since the probability is 0.0096

5 of 5 e)

probability =P(X>499)=P(Z>(499-467)/105)=P(Z>0.3)=1-P(Z<0.3)=1-0.6197=0.3803

it will not be because the probability that an individual gets a score greater than 499 is 0.3803