Answer:
Option (3)
Step-by-step explanation:
Therefore, Option (3) will be the correct option.
Peter was told by his teacher that he needed to measure the height of the building in which his classroom was located. He backs
1 answer:
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Using the normal distribution, it is found that:
a)
b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
c) Low: $23,519.65, High: $26,580.35.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
.
Hence the distribution of X can be described as follows:
The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the <u>p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200</u>, hence:
X = 33950:
Z = 0.73
Z = 0.73 has a p-value of 0.7673.
X = 14200:
Z = -0.91
Z = -0.91 has a p-value of 0.1814.
0.7673 - 0.1814 = 0.5859.
There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:
X - 25150 = -0.127(12050)
X = $23,519.65.
X - 25150 = 0.127(12050)
X = $26,580.35.
More can be learned about the normal distribution at brainly.com/question/4079902
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