According to a research? institution, men spent an average of ?$132.84 on?Valent

Question

According to a research? institution, men spent an average of
?$132.84
on?Valentine's Day gifts in 2009. Assume the standard deviation for this population is
?$45
and that it is normally distributed. A random sample of
10
men who celebrate? Valentine's Day was selected. Complete parts a through e.
a. Calculate the standard error of the mean.
sigma Subscript x overbar?xequals=nothing
?(Round to two decimal places as? needed.)
b. What is the probability that the sample mean will be less than
?$125??
Upper P left parenthesis x overbar less than $ 125 right parenthesisPx<$125equals=nothing
?(Round to four decimal places as? needed.)
c. What is the probability that the sample mean will be more than
?$140??
Upper P left parenthesis x overbar greater than $ 140 right parenthesisPx>$140equals=nothing
?(Round to four decimal places as? needed.)
d. What is the probability that the sample mean will be between
?$115
and
?$160160??
Upper P left parenthesis $ 115 less than or equals x overbar less than or equals $ 160 right parenthesisP$115?x?$160equals=nothing
?(Round to four decimal places as? needed.)
e. Identify the symmetrical interval that includes? 95% of the sample means if the true population mean is
?$132.84.
?$nothingless than or equals?x overbarxless than or equals??$nothing
?(Round to the nearest dollar as? needed.)

Explanation / Answer

a) Standard error = 45/SQRT(10)= 14.23

b) P(z<(125-132.84)/14.23

= 0.2908

c) P(z>(140-132.84)/14.23

= 0.3074

d) P((115-132.84)/14.23<z<(160-132.84)/14.23)

= 0.8669

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