# What is the probability that the sample mean will be within 1 hour of the population

#### ineedhelpinmathplease

The mean television viewing time for Americans is 15 hours per week (Money, November 2003). Suppose a sample of 60 Americans is taken to further investigate viewing habits. Assume the population standard deviation for weekly viewing time is σ = 4 hours.

 a. What is the probability that the sample mean will be within 1 hour of the population mean?
 b. What is the probability that the sample mean will be within 45 minutes of the population mean?

#### romsek

MHF Helper
Re: What is the probability that the sample mean will be within 1 hour of the populat

if you have an underlying population distribution with mean $\mu$ and standard deviation $\sigma$

and you take $N$ samples of that distribution and compute the mean of the sample, $\bar{X}$

then, provided $N$ is large enough $\bar{X}$ has an approximately normal distribution with mean $\mu$ and standard deviation $\dfrac{\sigma}{\sqrt{N}}$

In the given problem $N$ is large enough for this to be true.

given this you should be able to answer the questions.

#### ineedhelpinmathplease

Re: What is the probability that the sample mean will be within 1 hour of the populat

Thanks.

#### ineedhelpinmathplease

Re: What is the probability that the sample mean will be within 1 hour of the populat

 This is what I have so far 4/60= 0.0667 P[(14

#### sweetswimming

Re: What is the probability that the sample mean will be within 1 hour of the populat

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#### romsek

MHF Helper
Re: What is the probability that the sample mean will be within 1 hour of the populat

 This is what I have so far 4/60= 0.0667 P[(14
you scale $\sigma$ by $\dfrac {1}{\sqrt{N}}$

not $\dfrac{1}{N}$ as you have done.

otherwise it looks correct. See if you can use a table or some software to get the actual probability.

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