In a recent year, the ACT scores for high school students with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 25.7 and a standard deviation of 3.3. a) If a state university automatically admits the top 7% of students, what is the least score that a student can receive and still be admitted? b) In this same university, a student becomes ineligible for admission if he/she scores in the bottom 12%. What is the minimum score that a student needs to be eligible for admission? c) Find the probability that a randomly chosen high school student has an ACT score between 23 and 29.1.

In a recent year, the ACT scores for high school students with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 25.7 and a standard deviation of 3.3. a) If a state university automatically admits the top 7% of students, what is the least score that a student can receive and still be admitted? b) In this same university, a student becomes ineligible for admission if he/she scores in the bottom 12%. What is the minimum score that a student needs to be eligible for admission? c) Find the probability that a randomly chosen high school student has an ACT score between 23 and 29.1.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

In a recent year, the ACT scores for high school students with a 3.50 to 4.00 grade point average were
normally distributed, with a mean of 25.7 and a standard deviation of 3.3.
a) If a state university automatically admits the top 7% of students, what is the least score that a student
can receive and still be admitted?
b) In this same university, a student becomes ineligible for admission if he/she scores in the bottom 12%.
What is the minimum score that a student needs to be eligible for admission?
c) Find the probability that a randomly chosen high school student has an ACT score between 23 and
29.1.
d) If a sample of 25 students is randomly selected, find the probability that the average score of these
students lie between 23 and 29.1.
c) If 150 students are randomly selected, how many will have an ACT score that is more than 29.1?
f) What score represents the first quartile?
g) What is the 75th percentile of the ACT score?

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