Question

IQ tests are standardized and follow a normal distribution. On a common IQ test, the mean score is 100 with a standard deviation of 15.

a) What is the probability that a randomly selected individual gets a score of 105 or higher?
b) What are the mean and standard deviation of the average score of an SRS of 50 people? (Don't forget to justify this)
c) What is the probability that the average score of an SRS of 50 people is 105 or higher?

Answer 1

@jim_thompson5910

Answer 2

\[IQ=\frac{M_a}{C_a}*100\]
Ma = mental age, Ca = current age

Answer 3

we already did this problem no?

Answer 4

we did?

Answer 5

yes I think so

Answer 6

check your previous posts

Answer 7

I dont see it?

Answer 8

i have this tho:


(a)

= P (IQ - 100) /15 is greater than or equal to (105 - 100)/15)
= P(Z is greater than/equal to 0.33)
= 0.3707 <----

b)

Answer 9

is that right, and whats b and c? i dont think we did. maybe something similar

Answer 10

ok one sec

Answer 11

http://openstudy.com/users/schmidtdancer#/updates/51203204e4b03d9dd0c52253

Answer 12

same thing, just using different numbers

Answer 13

remember that problem?

Answer 14

It wont let me open it

Answer 15

is A right?

Answer 16

that's odd, try restarting your browser maybe?

Answer 17

i did:/

Answer 18

alright, one sec

Answer 19

kk

Answer 20

remember this calculator we used last time


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 21

yea!

Answer 22

remember how it works and how to use it?

Answer 23

i think lol

Answer 24

ok so what goes in the "mean" box?

Answer 25

for a right? and 100

Answer 26

standard dev= 15

Answer 27

good and good

Answer 28

now the left endpoint?

Answer 29

yes this is all for part a) for now

Answer 30

umm.. idk

Answer 31

0 ? or 105?

Answer 32

what's the smallest IQ you're considering

Answer 33

do you even care about the IQs less than 105 when looking at part a

Answer 34

no?

Answer 35

so 105 is the smallest

what's the largest?

Answer 36

ummmmm....

Answer 37

left endpoint=105. im not sure the right

Answer 38

the right endpoint is infinity since it goes on forever to the right (since we want 105 or greater ... we don't want it less than some value that is greater than 105)

but infinity isn't a number, so that won't work

however, you can just plug in a really large number in place of infinity...say 200

this number is definitely more than 3 standard deviations away from the mean

Answer 39

make sense?

Answer 40

ok so 200 for right

Answer 41

how do i know what my answer is for a, b, and c now?

Answer 42

yeah or some other big number that's definitely more than 3 std dev away from the mean

Answer 43

kk! so whats a?

Answer 44

ok did you type those 4 numbers in?

100
15
105
200

in that order

Answer 45

then you hit enter or the equals sign

Answer 46

yep!

Answer 47

ok what do you get

Answer 48

a ?

Answer 49

you got a number right?

Answer 50

theres different numbers,

Answer 51

idk which one to look at

Answer 52

ok see how it says

105 < z < 200

Answer 53

it's the number next to it is the one you want

Answer 54

yeah. is it .3694

Answer 55

? @jim_thompson5910

Answer 56

good, so that's your answer for part a

Answer 57

part b just wants the mean and std dev of the distribution of sample means (where the sample size is n = 50)

Answer 58

Xbar distribution

mean: xbar = mu

standard deviation: s = sigma/sqrt(n)

Answer 59

kk. so b is 100 for mean and 15 for sd?..

Answer 60

got half of that correct

Answer 61

ummm

Answer 62

mean = 100

standard deviation = sigma/sqrt(n)

standard deviation = 15/sqrt(50)

standard deviation = ???

Answer 63

Umm @jim_thompson5910

Answer 64

use calculator to find 15/sqrt(50)

Answer 65

2.12132

Answer 66

good

Answer 67

ok thanks! c?

Answer 68

answers to part b are 100 (mean) and 2.12132 (std dev)

Answer 69

ok thats what i put:D

Answer 70

now in part c, you go back to wolfram alpha and you type in

100
2.12132
105
200

notice how the only thing that has changed is the std dev

Answer 71

kk i did

Answer 72

.009211?

Answer 73

very good, getting the same

Answer 74

can u help with a few more PLZ @jim_thompson5910