The distribution of reading scores for 5th graders has mu = 92 and a standarddeviation = 22.a. If samples of n = 25 are selected at random, what value for the mean wouldseparate the top 10% of the samples?b. What is the probability of selecting a sample with a Mean of 92.6 or higher if n =55?c. What is the probability of selecting a sample with a mean between 90.5 and 92 if n= 67?d. Between what values for the mean would the middle 80% of the samples be if n =90?

As per the compony policy, solving more than 3 subparts in a single question is not allowed. Given, X~N(μ=92,σ2=222)a) When n=25 , p(Z<z)=0.90 Z0.9=1.28 .... By using Z table Now, x=μ+z.σn .... By using CLT x=92+1.28×2225 x=92+1.28×225 x=97.632 Hence, The value for the mean which separate top 10% is 97.63 b) p(x¯≥92.6)=p(x¯-μσ/n≥92.6-μσ/n) .... By using CLT =p(x¯-9222/55≥92.6-9222/55) =p(z≥0.20226) =1-p(z<0.20226) =1-0.580143 ..... By using Z table p(x¯≥92.6)=0.419857 Hence, Probability that sample mean equal to or more than 92.6 is 0.419857c) p(90.5<x¯<92)=p(90.5-μσ/n<x¯-μσ/n<92-μσ/n) .... By using CLT =p(90.5-9222/67<x¯-9222/67<92-9222/67) =p(-0.55809<z<0) =p(z<0)-p(z<-0.55809) =0.5-0.288391 ... By using Z table p(90.5<x¯<92)=0.211609 Hence, Probability that sample mean between 90.5 and 92 is 0.211609

Math

Statistics

The distribution of reading scores for 5" graders has mu = deviation = 22. 92 and a standard %3D a. If samples of n = 25 are selected at random, what value for the mean would separate the top 10% of the samples? %3D b. What is the probability of selecting a sample with a Mean of 92.6 or higher if n 55? %3D c. What is the probability of selecting a sample with a mean between 90.5 and 92 if n = 67? %3D

The distribution of reading scores for 5" graders has mu = deviation = 22. 92 and a standard %3D a. If samples of n = 25 are selected at random, what value for the mean would separate the top 10% of the samples? %3D b. What is the probability of selecting a sample with a Mean of 92.6 or higher if n 55? %3D c. What is the probability of selecting a sample with a mean between 90.5 and 92 if n = 67? %3D

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

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

The distribution of reading scores for 5th graders has mu = 92 and a standard
deviation = 22.
a. If samples of n = 25 are selected at random, what value for the mean would
separate the top 10% of the samples?
b. What is the probability of selecting a sample with a Mean of 92.6 or higher if n =
55?
c. What is the probability of selecting a sample with a mean between 90.5 and 92 if n
= 67?
d. Between what values for the mean would the middle 80% of the samples be if n =
90?

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