Yogurt manufacturers, food scientists; and government officials are also working together to develop additional solutions for re
1 answer:
You might be interested in
Answer:
a. 99.30% of the woman meet the height requirement
b. If all women are eligible except the shortest 1% and the tallest 2%, then height should be between 58.32 and 68.83
Explanation:
<em>According to the survey</em>, women's heights are normally distributed with mean 63.9 and standard deviation 2.4
a)
A branch of the military requires women's heights to be between 58 in and 80 in. We need to find the probabilities that heights fall between 58 in and 80 in in this distribution. We need to find z-scores of the values 58 in and 80 in. Z-score shows how many standard deviations far are the values from the mean. Therefore they subtracted from the mean and divided by the standard deviation:
z-score of 58 in= = -2.458
z-score of 80 in= = 6.708
In normal distribution 99.3% of the values have higher z-score than -2.458
0% of the values have higher z-score than 6.708. Therefore 99.3% of the woman meet the height requirement.
b)
To find the height requirement so that all women are eligible except the shortest 1% and the tallest 2%, we need to find the boundary z-score of the
shortest 1% and the tallest 2%. Thus, upper bound for z-score has to be 2.054 and lower bound is -2.326
Corresponding heights (H) can be found using the formula
and
Thus lower bound for height is 58.32 and
Upper bound for height is 68.83
Using the information given and the z-distribution, it is found that:
a) The point estimate of the population proportion is 0.5544.
b) The margin of error is: 0.0320.
c) The interval is: (0.5224, 0.5864).
d) The interpretation of the interval is: we are 95% sure that the true population proportion is between 0.5224 and 0.5864.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions has the bounds given by the rule presented as follows:
In which the variables used to calculated these bounds are listed as follows:
is the point estimate of the population proportion.
- z is the critical value.
- n is the sample size.
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of , so the critical value is z = 1.96.
From the sample, the sample size and the point estimate are given as follows:
The margin of error is given by:
M = 0.0320.
The interval is the point estimate plus/minus the margin of error, hence:
- Lower bound: 0.5544 - 0.0320 = 0.5224.
- Upper bound: 0.5544 + 0.0320 = 0.5864.
More can be learned about the z-distribution at brainly.com/question/25890103
#SPJ1