Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 27% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 85 freshmen is selected. Round the answer to at least four decimal places

1) It is appropriate to use the normal curve, since np = 22.95 ≥ 10 and n(1 - p) = 62.05 ≥ 10

2) The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline = 0.5832

Step-by-step explanation:

Concluding part of the question

1) Is it appropriate to use the normal approximation to find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline?

2) Find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline?

Solution

1) The condition for a distribution (binomial) to approximate a normal distribution is that

np ≥ 10 and n(1-p) ≥ 10

where n = sample size = 85

p = population proportion = sample proportion = 0.27

np = 85 × 0.27 = 22.95 ≥ 10

n(1-p) = 85 × 0.73 = 62.05 ≥ 10

2) To obtain the required probability, we need the standard deviation of the sampling distribution

σₓ = √[p(1-p)/n] = √(0.27×0.73/85) = 0.0481541642 = 0.04815

To obtain the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline, we need to standardize 28%

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (0.28 - 0.27)/0.04815 = 0.21

To obtain the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline

P(x < 0.28) = P(z < 0.21)

We'll use data from the normal probability table for these probabilities

P(x < 0.28) = P(z < 0.21) = 0.58317 = 0.5832 to 4 d.p

Hope this Helps!!!

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.