part a\na data set is normally distributed with a mean of 27 and a standard deviation of 3.5. find the z…

part a\na data set is normally distributed with a mean of 27 and a standard deviation of 3.5. find the z - score for a value of 25, to the nearest hundredth.\nz - score =\n\npart b\nin part a, about what percent of the data is greater than 34?\na. 48%\nb. 2%\nc. 4%\nd. 0.2%

part a\na data set is normally distributed with a mean of 27 and a standard deviation of 3.5. find the z - score for a value of 25, to the nearest hundredth.\nz - score =\n\npart b\nin part a, about what percent of the data is greater than 34?\na. 48%\nb. 2%\nc. 4%\nd. 0.2%

Answer

Answer:

Part A

-0.57

Part B

B. 2%

Explanation:

Part A

Step1: Recall z - score formula

$z=\frac{x-\mu}{\sigma}$

Step2: Substitute values

$x = 25$, $\mu=27$, $\sigma = 3.5$, so $z=\frac{25 - 27}{3.5}=\frac{-2}{3.5}\approx - 0.57$

Part B

Step1: Calculate z - score for 34

$z=\frac{34 - 27}{3.5}=\frac{7}{3.5}=2$

Step2: Use z - table

The area to the left of $z = 2$ is about 0.9772. So the area to the right (data greater than 34) is $1-0.9772 = 0.0228\approx2%$