Question

If the true proportion of customers who are below 20 years is p is equal to 0.35 ,what is the probability that a sample size 100 yields a sample proportion between 0.3 to 0.4

Answer 1

The probability that a sample size 100 yields a sample proportion between 0.3 to 0.4 is 0.7062819.

Step-by-step explanation:

Given : If the true proportion of customers who are below 20 years is p = 0.35

sample size : n= 100

Then , The probability that a sample size 100 yields a sample proportion between 0.3 to 0.4 :-

<tex>P(0.3<p<0.4)=P(\dfrac{0.3-0.35}{\sqrt{\dfrac{0.35(1-0.35)}{100}}}<z<\dfrac{0.4-0.35}{\sqrt{\dfrac{0.35(1-0.35)}{100}}})\ \ \ [\because \ z=\dfrac{\hat{p}-p}{\dfrac{p(1-p)}{n}}]\\\\=P(-1.05<z<1.05)\\\\=2P(z<1.05)-1\\\\=0.7062819</tex>

Hence, the probability that a sample size 100 yields a sample proportion between 0.3 to 0.4 is 0.7062819.

# Learn more :

If the probability of a win is 0.12 and the probability of a draw is 0.6, what is the probability of a loss?

https://brainly.in/question/7962977

Answer 2

Answer:

a fair coin is tossed 20 times and 12 heads needed means

we use combinations formula

²⁰C12/ 2²⁰

0.120