Question

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the standard error of the mean?

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns for this year is greater than 92?

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 100 returns is between 88 minutes and 92 minutes?

Answer 1

Answer 1

we have standard deviation= 14 and sampe size n = 100

using the formula standard error =

setting the given values, we get

Standard error = = 14/10 = 1.4

Answer 2

we have

we have to find the value of P(X more than 92)

using the formula P(X more than x) =

setting the given values, we get

P(X more than 92) =

this gives

So, required probability is 0.0764

Answer 3

we have

we have to find the value of P(X between 88 and 92)

using the formula =

setting the given values, we get

or

using normal distribution table, we can get the value of

So, = 0.8472