Question

**Moment Generating Functions**

A student's score on a Psychology exam has a normal distribution with mean 65 and standard deviation 10. The same student's score on a Chemistry exam has a normal distribution with mean 60 and standard deviation 15. The two scores are independent of each other. What is the probability that the student's mean score in the two courses is over 80?

**Before solving**, show that the mgf here is an
mgf of a Normal distribution. (Biggest confusion)

Answer #1

A student's score on a Psychology exam has a normal distribution .

A student's score on a Chemistry exam has a normal distribution .

The MGF of is

The MGF of is

The MGF is is

The MGF of is

Which is the MGF (since MGF is unique) of normal distribution with mean and variance

Hence the student's mean score in the two courses

Or

The probability,

In your psychology class, the mean exam score is 72 and
the standard deviation is 12. You scored 78.
In your biology class, the mean exam score is 56 and the
standard deviation is 5. You scored 66.
If your professors grade "on a curve" (i.e., according
to the distribution of scores), for which exam would you expect to
get a better grade?
(Hint: Convert your exam scores to
z-scores).
A) Biology
B) Psychology

The scores on a psychology exam were normally distributed with a
mean of 58 and a standard deviation of 9. What is the standard
score for an exam score of 57? The standard score is ______

Tom's psychology test score is +1 standard deviation from the
mean in a normal distribution. The test has a mean of 60 and a
standard deviation of 6. Tom's percentile rank would be
approximately ______________.
a. 70%
b. cannot determine from the information given
c. 84%
d. 66%

Test scores on an exam follow a normal
distribution with mean = 72 and standard deviation =
9. For a randomly selected student, find
a)
P(x ≥ 80), b) P(65 <x<90), what is thed minimum svore to be
among top 12 percent

9. The distribution of CHE 315 Exam I scores is nearly normal
with a mean of 72.6 points, and a standard deviation of 4.78
points. The test score of the top 5% of students in the class is
___________ and higher

The scores on the exam public health professionals take to be
certified follows a normal distribution with a mean score of 75
points and a standard deviation of 7 points.
What is the probability someone scores 71.5 or more on the
exam?

The scores on a college entrance exam have an approximate normal
distribution with mean, µ = 75 points and a standard deviation, σ =
7 points.
About 68% of the x values lie between what two values? What are
the z-scores?

The scores on the exam public health professionals take to be
certified follows a normal distribution with a mean score of 75
points and a standard deviation of 7 points.
What is the probability someone scores between 60 and 70?
Round your answer to 4 decimal places.

A normal distribution has a mean of 60 and a standard deviation
of 16. For each of the following scores, indicate whether the body
is to the right or the left of the score and find the proportion of
the distribution located in the body X = 64 X = 80 X = 52 X =
28

The mean score on a driving exam for a group of driver's
education students is 80 points, with a standard deviation of 5
points. Apply Chebychev's Theorem to the data using
kequals=2. Interpret the results.
At least __ % of the exam scores fall between __ and __
(Simplify your answers.)

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