Question

1) Find the z-score that most closely corresponds to the 45th percentile of values in a normal distribution.

2) The scores on a nationwide standardized exam are normally distributed. Let X = a score on the exam; X ~ N(150, 40).

Entry into a competitive program requires a score in the top 3% of test takers. If Jolynn wants to apply to this program, what is the minimum score she can earn to qualify?

Round your answer to the appropriate whole number.

3) The scores on a nationwide standardized exam are normally distributed. Let X = a score on the exam; X ~ N(150, 40).

Complete the statement:

____ % of test-takers will earn scores between 110 and 190.

Answer 1

Ans:

1)

P(Z<=z)=0.45

z=normsinv(0.45)

z=-0.1257

2)

For top 3%:

P(Z>z)=0.03

P(Z<=z)=1-0.03=0.97

z=normsinv(0.97)=1.881

minimum score to qualify=150+1.881*40=225.24

3)

110 and 190 are one standard deviation below and above the mean respectively.

For normal distribution,68% of the data falls within one standard deviation of the mean.

68% of the test-takers will earn scores between 110 and 190.