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According to a research​ institution, men spent an average of ​$ 134.63 on​ Valentine's Day gifts...

According to a research​ institution, men spent an average of ​$ 134.63 on​ Valentine's Day gifts in 2009. Assume the standard deviation for this population is ​$30 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.

b. What is the probability that the sample mean will be less than ​$130​?

c. What is the probability that the sample mean will be more than ​$145​?

d. What is the probability that the sample mean will be between ​$120 and ​$155​?

e. Identify the symmetrical interval that includes​ 95% of the sample means if the true population mean is ​$134.63.

$___ < x <$___

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