Question

An opinion poll asks an SRS of 1500 adults, "Do you happen to jog?" Suppose that the population proportion who jog (a parameter) is p = 0.15. To estimate p, we use the proportion p-hat in the sample who answer "Yes." Justify the use of a normal approximation and find the following probabilities.

a) P(p > 0.16)
b) P(0.14 < p < 0.16)

Answer 1

@jim_thompson5910

Answer 2

notice how

np = 1500*0.15 = 225

and how

n(1-p) = 1500(1-0.15) = 1275

Answer 3

ok

Answer 4

so because np > 5 and n(1-p) > 5, this allows us to use the normal distribution as an approximation to the binomial distribution given

Answer 5

ok

Answer 6

P(p>0.16) :

Answer 7

so instead of using that binomial distribution calculator from that last problem we did, we use the normal distribution calculator from wolfram alpha

Answer 8

Kk!

Answer 9

im there

Answer 10

ok p = 0.16 means 16%,

so take 16% of 1500 to get 0.16*1500 = 240

Answer 11

alright

Answer 12

240

Answer 13

now calculate the mean and std dev

mean: 1500*0.15 = 225
std dev: sqrt(1500*0.15*(1-0.15)) = 13.82932

Answer 14

kk did

Answer 15

ok now you type in these four values in the four boxes


225
13.82932
240
500 ... (or some other big number 3 std dev away from the mean)

Answer 16

kk i did

Answer 17

and you got what

Answer 18

.139

Answer 19

good

Answer 20

that's your answer to part a

Answer 21

ok:) now b?

Answer 22

?

Answer 23

14% of 1500 = ??

Answer 24

210

Answer 25

so that's your new left endpoint

your new right endpoint is 240

Answer 26

kk

Answer 27

is the answer 0.7219?

Answer 28

you got it

Answer 29

yay thanks! only a few multiple choice plz then im done i promise ahah