The diameter of small Nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches.Suppose a random sample of 20 balls is selected.Find the interval that contains 95.44 percent of the sample means.
A) $\left[ \begin{array} { l l }
5.04 & 5.36
\end{array} \right]$
B) $\left[ \begin{array} { l l }
5.18 & 5.22
\end{array} \right]$
C) $\left[ \begin{array} { l l }
5.16 & 5.24
\end{array} \right]$
D) $\left[ \begin{array} { l l }
5.07 & 5.33
\end{array} \right]$

Question

The diameter of small Nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches.Suppose a random sample of 20 balls is selected.Find the interval that contains 95.44 percent of the sample means.
A) $\left[ \begin{array} { l l } 
5.04 & 5.36
\end{array} \right]$
B) $\left[ \begin{array} { l l } 
5.18 & 5.22
\end{array} \right]$
C) $\left[ \begin{array} { l l } 
5.16 & 5.24
\end{array} \right]$
D) $\left[ \begin{array} { l l } 
5.07 & 5.33
\end{array} \right]$

Quizplus · Accepted Answer

We can use the formula for the confidence interval of the sample mean:

Confidence interval = sample mean ± (z-score)(standard error)

The standard error of the sample mean is equal to the standard deviation divided by the square root of the sample size:

standard error = 0.08 / sqrt(20) = 0.0179

To find the z-score that corresponds to a 95.44% confidence level, we can use a standard normal distribution table or calculator:

z-score = ±1.95996 (rounded to 5 decimal places)

Now we can plug in the values and calculate the interval:

Confidence interval = 5.2 ± 1.95996(0.0179) = [5.16, 5.24]

Therefore, the best choice is C, which contains the calculated interval.

The Diameter of Small Nerf Balls Manufactured at a Factory [5.045.36]\left[ \begin{array} { l l } 5.04 & 5.36\end{array} \right][5.04​5.36​]

The Diameter of Small Nerf Balls Manufactured at a Factory $\left[ \begin{array} { l l } 5.04 & 5.36\end{array} \right]$