Question

Nina is looking to analyze the distribution of the variable X=’grading. She gathered information from 1900 to 2000, and her data concludes X follows a normal distribution with mean 75 and variance 30.

1. What is the probability that a typical student from the current cohort enrolled receive a grade above 80?
2. Between what values will the grades of the 95% of all students in the current cohort fall?
3. Find the value that represents the 25^th and 75^th percentile of this distribution. Then, find the interquartile range. Can a student who got 45 be considered a potential outlier, explain the reasoning.

PLEASE SHOW EACH STEP AND EXPLAIN EACH STEP AS TO WHERE YOU ARE GETTING VALUES FROM (i.e., if you got value from z table, tell me why you use that table and where exactly). use mathematical formula as well as give me a reason why you used what formula you used.

Answer 1

Answer:

Given Data,

Nina is looking to analyze the distribution of the variable X=’grading.

She gathered information from 1900 to 2000, and her data concludes X follows a normal distribution with mean 75 and variance 30.

i.e, =75 and =30

So,==5.4772

The probability that a typical student from the current cohort enrolled receive a grade above 80:

Between what values will the grades of the 95% of all students in the current cohort fall:

With p-value=0.95 the corresponding Z-score lies between 1.96

Between 64.26 and 85.74.

The value that represents the 25^th and 75^th percentile of this distribution.Then, find the interquartile range:

With p-value=0.25 the corresponding Z-score=-0.674

With p-value=0.75 the corresponding Z-score=0.674

Interquartile range:

IQR=Q₃-Q₁

=78.69-71.31

=7.38

Therefore, interquartile range=7.38.

Can a student who got 45 be considered a potential outlier, explain the reasoning:

Given X=45

Then,

So,if is outlier i.e, 45 is outlier.