According to an IRS study, it takes a mean time of 330 minutes for taxpayers to

Question

According to an IRS study, it takes a mean time of 330 minutes for taxpayers to prepare, copy and electronically transfer a 1040 tax form. The population standard deviation of this distribution is 75 minutes. A consumer watchdog agency selects a random sample of 65 taxpayers for further study.

A. What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample mean for samples of size 65?

B. What is the probability that the sample mean is greater than 320 minutes?

Explanation / Answer

a) as the sample is for 65 so there will be a normal curve shape,

mean will be = 330

and standard deviation = 75/sqrt(65) = 9.30

b) p(x>320) =

For x = 320, z = (320 - 330) /9.30 = -1.07

Hence P(x > 320) = P(z > -1.07) = [total area] - [area to the left of -1.07]

1 - [area to the left of -1.07]

now from the z table we will take the value of z score = -1.07

    = 1 - 0.1423 = 0.8577

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