Question

The test scores for the analytical writing section of a particular standardized test can be approximated by a normal distribution, as shown in the figure. (a) What is the maximum score that can be in the bottom 10% of scores? (b) Between what two values does the middle 80% of scores lie? (a) The maximum score that can be in the bottom 10% is . (Round to two decimal places as needed.) (b) The middle 80% of scores lies between on the low end and (Round to two decimal places as needed.) on the high end.

Answer 1

Given, Mean, M= 3.3 Standard deviation, o=0.85 Here, P(Z <z) = 107 P(Zuz)=0.10 P(Z <=1-28155) = 0.10 Z: -1.28155 Now using z-score formula, to z*r & M (-1,29155) (0-85) + 3.3 - 2.2106825 202-21 b) Plazo czczo)= 0.80 & P (zazo)- PLZ L-Zo)= 0.80 2P ( Zazo)-1 a 0.80 P ( zczo)= 1.80 P(Z < Zo)= 0.90 Zo: 1.28155 Using z-score formula x Zur + = (1.28155) + (0.85)+ 3-3 ~ 4.09 * 7*+ M = 61.28155) (0,25) + 3.3 = 2.21