Question

Future scientists: Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 28% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 90 0 freshmen is selected. Round the answer to at least four decimal places.

Answer 1

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:

$\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.28*0.72}{90}}=\sqrt{0.0024}=0.047$

We can now calculate the z-score for 0.29 and 0.37

$z_1=\dfrac{p_1-p}{\sigma}=\dfrac{0.29-0.28}{0.0047}=\dfrac{0.01}{0.0047}=2.13\\\\\\z_2=\dfrac{p_2-p}{\sigma}=\dfrac{0.37-0.28}{0.0047}=\dfrac{0.09}{0.0047}=19.15$

Now, we can calculate the probability as:

$P(0.29$