An intelligence scale for children is approximately normally distributed, with mean 100 and standard deviation 15. rs 7, 8, and 9earchKAn intelligence scale for children is approximately normally distributed, with mean 100 and standard devClick here to view page 1 of the standard normal distribution table. Click here to view page 2 of the stanc<(a) What is the probability that a randomly selected test taker will score above 125?Question 2 of 20 >(Round to four decimal places as needed.)(b) What is the probability that a randomly selected test taker will score below 90?(Round to four decimal places as needed.)(c) What proportion of test takers will score between 110 and 140?(Round to four decimal places as needed.).(d) Would it be unusual for a randomly selected child to have a score above 150?Obecause P(X>150) =(Round to four decimal places as needed.)(e) What intelligence score will place a child in the 98th percentile?1040hpC...4

It is given that Mean = 100 Standard deviation = 15 Note: According to Bartleby expert guidelines, we can answer only first question with their three subparts and rest of the question reposted.Solution(a): P( X > 125 ) = P[( X - μ )/σ > (125 - 100)/15] = P( Z > 1.667 ) = 0.047757 = 0.0478 ( round upto 4 decimal places ) Note: The Excel function is: =1-NORM.S.DIST(1.667,TRUE)Solution(b) P( X < 90 ) = P[( X - μ )/σ < (90 - 100)/15] = P( Z < -0.667 ) = 0.25239 = 0.2524 ( round upto 4 decimal places ) Note: The Excel function is: =NORM.S.DIST(-0.667,TRUE)Solution(c): P( 110 < X < 140 ) = P[(110 - 100)/15 < ( X - μ )/σ < (140 - 100)/15] = P( 0.667 < Z < 2.667 ) = P( Z < 2.667 ) - P( Z < 0.667 ) = 0.99617 - 0.74761 = 0.24856 = 0.2486 ( round upto 4 decimal places ) Note(1). The Excel function for P( Z < 2.667 ) =NORM.S.DIST(2.667,TRUE) (2). The Excel function for P( Z < 0.667 ) =NORM.S.DIST(0.667,TRUE)

Answered: (a) What is the probability that a…

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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An intelligence scale for children is approximately normally distributed, with mean 100 and standard deviation 15.

rs 7, 8, and 9
earch
K
An intelligence scale for children is approximately normally distributed, with mean 100 and standard dev
Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the stanc
<
(a) What is the probability that a randomly selected test taker will score above 125?
Question 2 of 20 >
(Round to four decimal places as needed.)
(b) What is the probability that a randomly selected test taker will score below 90?
(Round to four decimal places as needed.)
(c) What proportion of test takers will score between 110 and 140?
(Round to four decimal places as needed.).
(d) Would it be unusual for a randomly selected child to have a score above 150?
O
because P(X>150) =
(Round to four decimal places as needed.)
(e) What intelligence score will place a child in the 98th percentile?
10
40
hp
C...
4

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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