A. About_____ % of the area under the curve of the standard normal distribution
ID: 3056444 • Letter: A
Question
A. About_____ % of the area under the curve of the standard normal distribution is between z=1.404z=-1.404 and z=1.404z=1.404 (or within 1.404 standard deviations of the mean). Round your answer to two decimal places.
B. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 48 months and a standard deviation of 8 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 56 and 64 months?
C. A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1053 and a standard deviation of 202. Scores on the ACT test are normally distributed with a mean of 20.3 and a standard deviation of 4.6. It is assumed that the two tests measure the same aptitude, but use different scales.
If a student gets an SAT score that is the 29-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.
What would be the equivalent ACT score for this student?
ACT score =
Round answer to 1 decimal place.
If a student gets an SAT score of 1417, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.
Explanation / Answer
A) P(-1.4 < Z < 1.4) = P(Z < 1.4) - P(Z < - 1.4) = 0.9192 - 0.0808 = 0.8384 = 83.84%
B) mean = 48
Sd = 8
Z = (X - mean) /sd
P(56 < X < 64) = P((56-48)/8 < Z < (64-48)/8)
= P(1 < Z < 2)
= (95 - 68)/2
= 13.5%
C) Z score for 29 percentile = - 0.55
SAT score = 1053 - 0.55 * 202 = 941.9
ACT score = 20.3 - 0.55 * 4.6 = 17.8
Z score for 1417 = (1417 - 1053) / 202 = 1.8
ACT score = 20.3 + 1.8 * 4.6 = 28.6
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.