Question

10. Test scores fo standard deviation of 8. or a standardized math test follow a ormal distribution with a mean of 73 and a 。. { A random sample of 23 students took this math test. What is the probalility t random the average score of the 23 students falls above 757 -.849 s lo 11S 11. In the population of male students, motivation soores follow a normal distribution with an average of 32.4 and a standard deviation of 7. A ranlom sample of 16 male students is to be taken. They asked to answer the motivation questionnaire so that their motivation soores can he determined. the probability that the sample mean score will not exceed 357 ,o 68
Can someone help me with number 11? The answer is suppose to be 0.0681

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	32.400
std deviation   =σ=	7.0000
sample size       =n=	16
std error=σx̅=σ/√n=	1.7500

thefore probability that sample mean score will nor excced 35 =P(Xbar< 35) =P(Z<(35-32.4)/1.75)

=P(Z<1.49) =0.9313 ( this should be 0.9313 and not 0.0681; actually 0.0681 is probability that sample mean is greater than 35)

(please revert for any clarification required)