Answer:
The probability that the proportion of freshmen in the sample of 150 who plan to major in a STEM discipline is between 0.29 and 0.37 is 0.3855
Step-by-step explanation:
The probability that the proportion of freshmen in the sample of 150 who plan to major in a STEM discipline is between 0.29 and 0.37 can be calculated by finding <em>z-scores</em> and subtracting P(z<z(0.29)) from P(z<z(0.37))
z-score in the binomial distribution of 28% of freshmen entering college in a recent year planned to major in a STEM discipline can be calculated using the equation:
where
- p(s) is proportion of freshmen we are interested (0.37, 0.29)
- p is the proportion found in recent year found by research group (28% or 0.28)
- N is the sample size (150)
Then z(0.37)= ≈ 2.4550 and P(z<2.4550)=0.993
z(0.29)= ≈ 0.2728 and P(z<0.2728)=0.6075
Then P(z(0.29)<z<z(0.37))=0.993-0.6075=0.3855