Respuesta :
Answer:
The probability that the proportion of freshmen in the sample of 90 who plan to major in a STEM discipline is between 0.29 and 0.37 is P=0.0166.
Step-by-step explanation:
The question is incomplete. You have to add:
Find the probability that the proportion of freshmen in the sample of 90 who plan to major in a STEM discipline is between 0.29 and 0.37.
We have a sample of n=90 out of a population with a proportion p=0.28.
We have to calculate the probability that the sample has a proportion between 0.29 and 0.37.
First, we calculate the standard deviation of the sampling distribution:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.28*0.72}{90}}=\sqrt{0.0024}=0.047[/tex]
We can now calculate the z-score for 0.29 and 0.37
[tex]z_1=\dfrac{p_1-p}{\sigma}=\dfrac{0.29-0.28}{0.0047}=\dfrac{0.01}{0.0047}=2.13\\\\\\z_2=\dfrac{p_2-p}{\sigma}=\dfrac{0.37-0.28}{0.0047}=\dfrac{0.09}{0.0047}=19.15[/tex]
Now, we can calculate the probability as:
[tex]P(0.29<\hat p<0.37)=P(2.13<z<19.15)=P(z<19.15)-P(z<2.13)\\\\P(0.29<\hat p<0.37)=1-0.9834=0.0166[/tex]
