91影视

Given in the question that

Number of songs in the iPod $=10000$

Mean$=225$seconds

Standard deviation $=60$seconds

Number of songs in SRS$=10$

we have to find ow many songs would you need to sample if you wanted the standard deviation of the sampling distribution of $\stackrel{炉}{x}$to be$30$seconds.

The mean of the sampling distribution of $\stackrel{铃�}{p}is{渭}_{\stackrel{铃�}{p}}=p$

The standard deviation of a sample distribution of the sample mean $\overline{x}$if the population standard deviation is $蟽$can be written as,

${蟽}_x=\frac{蟽}{\sqrt{n}}$

Here, number of songs to sample is the sample size.

Also,

Population standard deviation, $蟽=60$

Standard deviation of the sample, ${蟽}_{\stackrel{炉}{x}}=30$

It is known that the standard deviation of a sample distribution of the sample mean $\stackrel{炉}{x}$if the population standard deviation is $蟽$can be written as,

${蟽}_{\stackrel{炉}{x}}=\frac{蟽}{\sqrt{n}}$

To find the sample size, use the above formula.

Write the formula as:

${蟽}_{\stackrel{炉}{x}}=\frac{蟽}{\sqrt{n}}$

$\sqrt{n}=\frac{蟽}{{蟽}_{\stackrel{炉}{x}}}$

square both sides of the equation

$n=\frac{{蟽}^2}{{{蟽}_{\stackrel{炉}{x}}}^2}$

substitute $60for蟽and30for{蟽}_{\stackrel{炉}{x}}$in the aboveexpression and simplify for $n$

$n=\frac{{60}^2}{{30}^2}=4$

Hence, the requirred number of songs to sample is $4$