Question

The distribution of scores for persons over 16 years of age on a Wechsler Adult Intelligence Scale (WAIS) is approximately normal with mean 100 and standard deviation 15. The WAIS is one of the most common "IQ tests" for adults.

a) What is the probability that a randomly chosen individual has a WAIS score of 105 or higher?
b) What are the mean and standard deviation of the average WAIS score x for an SRS of 60 people?
c) What is the probability that the average WAIS score of an SRS of 60 people is 105 or higher?

Answer 1

d) Would your answers to any of (a), (b), or (c) be affected if the distribution of WAIS scores in the adult population were distinctly non-normal?

Answer 2

@jim_thompson5910

Answer 3

I think I asked this before, but I'm not sure

Answer 4

but do you have a TI calculator?

Answer 5

I do not, sorry

Answer 6

that's ok, we'll just use wolfram alpha

Answer 7

one sec

Answer 8

kk!

Answer 9

ok first go to this page

http://www.wolframalpha.com/input/?i=normal+cdf&a=*MC.normal+cdf-_*Formula.dflt-&f2=0&f=NormalProbabilities.mu_0&f3=0&f=NormalProbabilities.l_0&f4=1&f=NormalProbabilities.r_1&a=*FVarOpt.1-_***NormalProbabilities.l-.*NormalProbabilities.r--.***NormalProbabilities.z--.**NormalProbabilities.pr---.**NormalProbabilities.mu---&a=*FVarOpt-_**NormalProbabilities.sigma-.*NormalProbabilities.l-.*NormalProbabilities.r-.*NormalProbabilities.mu--

Answer 10

ok

Answer 11

then you enter 100 in the box next to the mean

Answer 12

15 next to standard deviation

Answer 13

those boxes will stay the same throughout this problem

Answer 14

with me so far?

Answer 15

i did that

Answer 16

ok great

Answer 17

for part a)

you'll type 105 in the "left endpoint" box

then you'll type some very large number that is more than 3 std dev away from the mean...so say 170 into the "right endpoint" box

Answer 18

oh my bad, the std dev will change for part b

but don't worry about that right now

Answer 19

ok

Answer 20

I did that and hit enter, I'm not seeing anything

Answer 21

all of the values have been typed in the correct boxes right?

Answer 22

if so, then click on one box and click on the equals sign that pops up to the right of the box you clicked on

Answer 23

yes

Answer 24

did you click on the equals sign?

Answer 25

i did that

Answer 26

and nothing?

Answer 27

no just a graph and table

Answer 28

ok in the "probabilities" table

what is the last entry in the 2nd column?

Answer 29

.3694?

Answer 30

perfect, got the same thing

Answer 31

Ok:)

Answer 32

so that's the probability that you pick someone with a 105 or higher

Answer 33

ok! cool

Answer 34

sadly you can't just input 105 then tell it to go to infinity

but you can make the right endpoint something so big that you're pretty much going to infinity as far as the distribution is concerned

Answer 35

ok, what should i put for b

Answer 36

for b the mean will stay the same

but the std dev will change

Answer 37

ok, what do i use for the std

Answer 38

the new standard deviation is found by this formula

s = sigma/sqrt(n)

s = 15/sqrt(60)

s = 1.93649

Answer 39

so 1.93649 is the new std dev

Answer 40

ok so i use 1.93649 for the std?

Answer 41

so when it asks

What are the mean and standard deviation of the average WAIS score x for an SRS of 60 people

Answer 42

I got .0049

Answer 43

the answers are

100 and 1.93649

Answer 44

0.004912?

Answer 45

no you're not computing probabilities here

just finding the mean and std dev

Answer 46

make sense?

Answer 47

ohhok

Answer 48

so what would b be then?

Answer 49

yeah no need for wolfram alpha for part b

Answer 50

100 and 1.93649

Answer 51

yep

Answer 52

mean stays the same, std changes to that

Answer 53

mean = 100 , std1,93649

Answer 54

ok now c??

Answer 55

I plug in 100 for mean, but what about the rest?

Answer 56

@jim_thompson5910 ?

Answer 57

one sec lol sry getting info

you use 100 for mean, 1.93649 for std dev

Answer 58

ok i did

Answer 59

105 for left box
170 for right box

Answer 60

170 should be plenty large enough

Answer 61

is it .004912?

Answer 62

you got it

Answer 63

ok yay! now d?

Answer 64

so what part c is saying is that if you have a random sample of 60 people, then the chances of the mean of this sample being higher than 105 is 0.004912

Answer 65

Yea:)

Answer 66

hmm let me think d over

Answer 67

kk

Answer 68

I would think so, but I'm not 100% sure

normal distributions are hard enough to compute let alone something non-normal

the reason I think so is because let's say that the distribution was right skewed. This would mean that there are extremes to the right pulling the distribution and stretching it to the right, which would mean that the bulk of the distribution would lie on the left

so that would diminish the probabilities in my opinion

Answer 69

it's hard to say because there are a ton of non-normal distributions out there, but I think for the most part, the non-normalness would change the probabilities

Answer 70

so would the answers be affected?

Answer 71

is this good> (d) I believe that the non-normalness would change the probabilities.

Answer 72

yes I would think so

sure there may be some non-normal distributions that "look" like the normal distribution (on some level), but the majority of them look different

Answer 73

hmm I guess non-normalness is a strange way to put it

Answer 74

ok thanks so much! how would i put it

Answer 75

I would say

If the IQs were distributed on some non-normal distribution, then the probabilities would change because the overall graph of the distribution would change. For instance, the graph may be more skewed right which would alter the probabilities.

Answer 76

ok thanks so much!! i have one more problem, can i type it here?

Answer 77

non-normalness i guess is just a slang or quick way to say that a distribution is not normal

Answer 78

sure

Answer 79

I'll start with a :

The distribution of scores for persons over 16 years of age on a Wechsler Adult Intelligence Scale (WAIS) is approximately normal with mean 100 and standard deviation 15. The WAIS is one of the most common "IQ tests" for adults.

a) What is the probability that a randomly chosen individual has a WAIS score of 105 or higher?

Answer 80

is this the same problem?

Answer 81

oops haha

Answer 82

lol deja vu...

Answer 83

Only a and b: A laboratory weighs filters from a coal mine to measure the amount of dust in the mine atmosphere. Repeated measurements of the weight of dust on the same filter vary normally with a standard deviation of 0:08 milligram (mg) because the weighing is not perfectly precise. The dust on a particular filter actually weighs 123 mg. Repeated weighings will then have the normal distribution with mean 123 mg and standard deviation 0.08 mg.

a) The laboratory reports the mean of 3 weighings. What is the distribution of this mean?
b) What is the probability that the laboratory reports a weight of 124 mg or higher for this filter (the one that was weighed 3 times)?

Answer 84

LOL

Answer 85

you're just doing that to see if i was awake or testing my IQ lol

Answer 86

hahaha

Answer 87

when you say 0:08 did you mean 0.08 ?

Answer 88

I'll assume you did

Answer 89

I think yeah

Answer 90

n=3
x= measurements of the weight of dust on same filter

X : n (123; 0.08)

-- n (123; 0.08/sqrt(3)

-- 0.08/sqrt(3)
= 0.046 <-----

Answer 91

what i got

Answer 92

very good, so it would be N(123, 0.046)

that's the distribution for the means of the samples of size 3

Answer 93

ok!! how d i do b..

Answer 94

very small sample, I would definitely bump it up if this was in the real world

Answer 95

yeah

Answer 96

hey christinee!!!!!!!!!!!! lol using this too

Answer 97

Chandler!!!! Haha hey:D

Answer 98

LOL i dies when i saw your name here