Question

A variable is normally distributed with mean 23 and standard deviation 4. Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed.a) Find the area to the left of 25. b) Find the area to the left of 18. c) Find the area to the right of 23. d) Find the area to the right of 28. e) Find the area between 18 and 30. (b) Find the probability that the percent of fat calories a person consumes is more than 38. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place).Shade: Left of a value. Click and drag the arrows to adjust the values. Normal curveInterval pointer-1.5(d) Find the maximum number for the lower quarter of percent of fat calories. Round your answer to 3 decimal places. (e) Sketch the graph and write the probability statement.

Answer 1

a)

In order to calculate the area to the left of 25, first let's find the z-value using the formula below:

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

Where x = 25, the mean is equal to 23 and the standard variation is equal to 4.

So we have:

$z=\frac{25-23}{4}=\frac{2}{4}=0.5$

Looking at the z-table for the probability of z <= 0.5, we have 0.6915, so the area to the left of 25 is equal to 0.6915.