Question

Opinions on health care reform range on a scale from 0 (the respondent favors a plan based on private medical insurance) to 20 (the respondent favors a government based plan) and the data is normally distributed. The mean score of the responses to this question is a 11 with a standard deviation of 2.7.

A. What is the probability that a score ranges between 7 and 10?

B. What is the minimum score a person needs to be in the top 15%?

C. Approximately 95% of data would fall between what two scores?

Answer 1

Solution :

Given that ,

mean = = 11

standard deviation = = 2.7

(A)

P(7 < x < 10) = P[(7 - 11)/ 2.7) < (x - ) /  < (10 - 11) / 2.7) ]

= P(-1.48 < z < -0.37)

= P(z < -0.37) - P(z < -1.48)

= 0.3557 - 0.0694

= 0.2863

B)

P(Z < 1.04) = 0.85

z = 1.04

Using z-score formula,

x = z * +

x = 1.04 * 2.7 + 11 = 13.808

Minimum score = 13.808

C)

The 95% has the z values are : -1.96 and +1.96

x = -1.96 * 2.7 + 11 = 5.708

x = 1.96 * 2.7 + 11 = 16.292

Two scores are : 5.708 and 16.292