The gestation time of humans has an approximate Normal distribution with a mean of 250 days and a standard deviatim- 6.0 days. A simple random sample of n newborns is to be taken. What is the minimum sample sized needed so that the sampling distribution of bar(x) has a standard deviation of 0.5 day? 15 144 12 250

Identify Formula: Step 1: Identify the formula to find the minimum sample size needed to achieve a specific standard deviation of the sample mean. The formula is $ n = \left(\frac{\sigma}{\text{desired standard deviation}}\right)^2 $ where $ \sigma $ is the population standard deviation. Plug in Values: Step 2: Plug in the values into the formula. Here, $ \sigma = 6.0 $ days (given as the standard deviation of the population), and the desired standard deviation of the sample mean is 0.5 day. So, $ n = \left(\frac{6.0}{0.5}\right)^2 $. Calculate Inside Parentheses: Step 3: Calculate the value inside the parentheses first. $ \frac{6.0}{0.5} = 12.0 $. Square Result: Step 4: Now, square the result from Step 3 to find $ n $. $ 12.0^2 = 144 $.

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The gestation time of humans has an approximate Normal distribution with a mean of $250$ days and a standard deviatim- $6$ . $0$ days. A simple random sample of $n$ newborns is to be taken. $\newline$ What is the minimum sample sized needed so that the sampling distribution of $\bar{x}$ has a standard deviation of $0$ . $5$ day? $\newline$ $15$ $\newline$ $144$ $\newline$ $12$ $\newline$ $250$

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Q. The gestation time of humans has an approximate Normal distribution with a mean of

250

days and a standard deviatim-

6

0

days. A simple random sample of

n

newborns is to be taken.

\newline

What is the minimum sample sized needed so that the sampling distribution of

\bar{x}

has a standard deviation of

0

5

day?

\newline

15

\newline

144

\newline

12

\newline

250

Identify Formula: Step $1$ : Identify the formula to find the minimum sample size needed to achieve a specific standard deviation of the sample mean. The formula is $n = \left(\frac{\sigma}{\text{desired standard deviation}}\right)^2$ where $\sigma$ is the population standard deviation.
Plug in Values: Step $2$ : Plug in the values into the formula. Here, $\sigma = 6.0$ days (given as the standard deviation of the population), and the desired standard deviation of the sample mean is $0$ . $5$ day. So, $n = \left(\frac{6.0}{0.5}\right)^2$ .
Calculate Inside Parentheses: Step $3$ : Calculate the value inside the parentheses first. $\frac{6.0}{0.5} = 12.0$ .
Square Result: Step $4$ : Now, square the result from Step $3$ to find $n$ . $12.0^2 = 144$ .