Answer:
a) Probability of a randomly sampled women not being qualified for the internship = 0.223
b) Probability that at least 30 percent of the women in the sample will not meet the age requirement for the internships = 0.03216
c) A woman who does not meet the age requirement is more likely to be selected with a stratified random sample than with a simple random sample.
Step-by-step explanation:
Age | Probability
17 | 0.005
18 | 0.107
19 | 0.111
20 | 0.252
21 | 0.249
22 | 0.213
23 or older | 0.063
a) Only 20+ year olds are qualified for the internship
So, probability of being qualified for the internship = P(x ≥ 20)
Probability of not being qualified for the internship = P(x < 20) = P(x=17) + P(x=18) + P(x=19) = 0.005 + 0.107 + 0.111 = 0.223
b) According to the Central limit theorem, a sampling distribution of sample size as large as 100 selected from this population distribution will approximate a normal distribution. It also has that
Mean proportion of sampling distribution of women who do not meet the internship requirements = Population proportion of women who do not meet the internship requirements = p = 0.223
The standard deviation of the is given by
σₓ = √[p(1-p)/n]
n = sample size = 100
σₓ = √[(0.223×0.777)/100] = 0.041625833 = 0.04163
So, to obtain the probability that at least 30 percent of the women in the sample will not meet the age requirement for the internships
P(x ≥ 0.30)
We first standardize 0.30
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (0.30 - 0.223)/0.04163 = 1.85
The required probability
P(x ≥ 0.30) = P(z ≥ 1.85)
We'll use data from the normal probability table for these probabilities
P(x ≥ 0.30) = P(z ≥ 1.85) = 1 - P(z < 1.85)
= 1 - 0.96784 = 0.03216
c) Probability of women not meeting the internship requirements = 0.223
Probability of women meeting the internship requirements = 1 - 0.223 = 0.777
Or
Probability of women meeting the internship requirements = P(x ≥ 20)
= P(x=20) + P(x=21) + P(x=21) + P(x ≥ 23) = 0.777
But as the stratified sample only contains women who do not meet the internship requirements, it is more likely that A woman who does not meet the age requirement is selected with a stratified random sample than with a simple random sample.
Hope this Helps!!!
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