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# Normal distribution

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These are questions from a past paper that Iam lost with. Can you do each question in a way that is broken down into simple steps leading to the answer. It is important to me that each step is shown clearly. please help im fed up of this battle with stats.

1)IQ of people normally distributed with mean 120
and standard deviation (SD) of 25
Calculate the probability that an adult will have

a)less than 100
b)greater than 150
b)between 100 and 150

c)Any person with a score over 200 is considered a genius. In a population of 10000 how many will score 200.

d)MENSA is a set up to recuit the top 1% population. What should the IQ score be set at to qualify for mebership?

2. A chemical company produces a product which has an impurity whish is expensive to remove. The mean level is 20 parts per million with SD of 6 parts.

a)What level of impurity could the chemical company quote to customeas and be 99% conficent that it will not exceed?

A customer, however, is only prepared to accept a maximum impurity of 30 parts.

b)How much product will meet this specification?

c)Suppose the product deteriorates so that the mean drifts out to 25 parts per million, but with the same SD of 6 parts. How much of production is now unsuitable?

d)Finally, if the mean is brought bvack to 20 parts but the SD is the found to be 8 parts, how much product will not meet the specification?

3. During tests on a gruop of workers it is found that only 15% of them can hear sound above a frequency of 200 units and ony 6% can dewtect sound above 210 units.
Calculate the mean and SD of the highest frequency that can be heard for the population of workers

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## SOLUTION This solution is FREE courtesy of BrainMass!

Note: In order to do Normal distribution problems , you should first calculate Z Values , which is given by : (x-Mean)/std dev. Here x is the variable ( for eg in Q1 it asks less than 100 , x will be 100 here). After caluculating the Z value we can look up the probability from the Normal tables.
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<br>Also if the Probability is given ( like how many samples will conform to 99% , then we look up the Z value from the tables and determine the limits.
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<br>I have answered all the questions using Excel ( it has nice capabilities to do all the normal distribution problems using commands). I have used cell referencing while giving command in excel so that it helps.
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<br>Note: When we use Normdist command , it gives us the probability directly without having to worry about the Z scores and look up the tables. The input it takes is , X value, Mean, STD Dev and Cumulative ( it means that it will the probability of values below the value of X).

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com September 26, 2022, 6:40 pm ad1c9bdddf>
https://brainmass.com/statistics/normal-distribution/normal-distribution-12901