Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of nequals70?, find the probability of a sample mean being greater than 215 if muequals214 and sigmaequals5.8. For a sample of nequals70?, the probability of a sample mean being greater than 215 if mu equals 214 and sigmaequals5.8 is 0.9251. ?(Round to four decimal places as? needed.) Would the given sample mean be considered? unusual? The sample mean would would would not be considered unusual because it lies does not lie lies within the range of a usual? event, namely within 3 standard deviations 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means.

Answer 1

for normal distribution z score =(X-)/
here mean=      =	214
std deviation   ==	5.800

sample size       =n=	70
std error=x?=/n=	0.6932

probability =

P(X>215)

=

P(Z>1.44)=

1-P(Z<1.44)=

1-0.9254=

0.0749

he sample mean would not be considered unusual because it   does lies within the range of a usual? event  namely within  2 standard deviations  of the mean of the sample means.