Question

In a survey, 600 mothers and fathers were asked about the importance of sports for
boys and girls. Of the parents interviewed, 70% said the genders are equal and should
have equal opportunities to participate in sports.
Using the normal approximation, what's the probability a randomly drawn
sample of parents of size 600 will have a sample proportion between 67% and
73%? Draw a sketch of the probability curve, shade the area representing the
probability you're finding, and label the z-scores that represent the upper and
lower bounds of the probability you're finding.

Answer 1

the mean is .7 and the sd=0.0187 N(.7,0.0187) I just don't know what to do from here, also can't use the continuity correction.

Answer 2

so are you aware with normal distribution?

Answer 3

i know what the normal distribution is if thats what your asking? @faiqfaees

Answer 4

okay very good.
can you calculate the shaded area

Answer 5

you would need to find the zscores of each right? @faiqraees

Answer 6

yes

Answer 7

oh i am sorry 0.63 will lie on the other side (negative x axis)

Answer 8

I got -3.743315508 for .63 and 1.604278075 for .73 is that right?

Answer 9

@faiqraees

Answer 10

well I actually dont have access to the areas to the values of z right now but if you send me the method you applied I can verify it for you.

Answer 11

i just did x-mean/sd for both @faiqraees

Answer 12

then it should be correct

Answer 13

okay so are those the zscore values that represent the lower and upper bounds of the probabiliity? @faiqraees

Answer 14

now use the identity
total probability = (first prob. +second prob.) - 1

Answer 15

that way you will have the answer

Answer 16

okay so -3.743315508 + 1.604278075 -1 = -3.139037433 @faiqraees so is that the probability of drawing between 67% and 73%?

Answer 17

oh no no after taking those z values you have to calculate their areas using the normal distribution function chart.

Answer 18

okay so what do I do with the -3.139037433 or did i not need to find that @faiqraees

Answer 19

you dont need that
just find the normal distribution values for -3.743315508 and 1.604278075

Answer 20

okay so just find their z-scores then? @faiqraees

Answer 21

no find the area under the curve if you integrate the function with negative infinity and z value

Answer 22

do you have a normal distribution function chart or something

Answer 23

no i dont but i can probably find one on the internet @faiqraees

Answer 24

i dont know how to find one for -3.74 but for 1.604278075 i got .4452 but i dont know if thats right? @faiqraees

Answer 25

for 1.6 one the answer is 0.9456 and i cant also find the values for -3.74. Its above the range of my chart. Try googling its value

Answer 26

for -3.7 it says .00011 but that doesnt seem right @faiqraees

Answer 27

there are many kind of normal distribution are you sure you're checking the right one?

Answer 28

It just said standard normal distribution table: Table Values Represent AREA to the LEFT of the Z score. I don't know haha @faiqraees

Answer 29

how about checking the value of 1.604278075 through it. If it shows the value you're concerned with then thats the correct answer

Answer 30

for 1.6 is shows .94520 @faiqraees

Answer 31

ok wait let me work out the value using integration

Answer 32

for -3.74 just do 1- 0 .00011

Answer 33

okay so we have .9456 and 0.99989 so would we add them then subtract 1? @faiqraees

Answer 34

yes to find the answer

Answer 35

okay thank you so much