Question

Ninety-five percent of students at an elementary school are between 3.6 feet tall and 5.5 feet tall. Assume the height data at this school is normally distributed. Use the normal curve below and the empirical rule to find the mean and then the standard deviation for the height data. Round to two decimal places.

Answer 1

Mean= 4.55

Standard Deviation= 0.48

Answer 2

Answer:4.55,0.47

Explanation:

Given height varies from 3.6 feet to 5.5 feet for 95% student

i.e.

95% data falls in the interval of (\mu -2\sigma ,\mu +2\sigma )

So

`\mu -2\sigma=3.6`-----------(1)

`\mu +2\sigma=5.5` -----------(2)

Solving (1)&(2) we get

`\mu =4.55`

`\sigma =0.475`

Thus mean=4.55

And standard deviation=0.47