Heights of fourth graders are Normally distributed with a mean of 52 inches and a standard deviation of 3.5 inches. What percentage of fourth graders are between 50 inches and 56 inches? A. 68.13% B. 27.42% C. 59.01% D. 95.27% E. 86.43%

C. 59.01%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

What percentage of fourth graders are between 50 inches and 56 inches?

This is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

X = 56

has a pvalue of 0.8729

X = 50

has a pvalue of 0.2843.

0.8729 - 0.2843 = 0.5886, which is close to 59.01%.

So the correct answer is:

C. 59.01%

cosine

step-by-step explanation:

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8