The grade scored by Mehmet in a course is normally distributed with a mean of 50 and standarddeviation of 4.a) If the probability that Mehmet will pass from this course is 0.8413, what is the passing grade? (Notethat to pass from a score, a student should score a grade which is higher than the passing grade.)b) The grade scored by another student from the same course is again normally distributed with a meanof 56 and standard deviation of 3. Find the probability that this student will score higher grade thanMehmet. A parent has their child in daycare twice a week. Being busy people they are often a few minutes lateto pick her up. The daycare has a strict policy that parents need to be on time. They enforce this bycharging 1 dollar per minute for tardiness (late arrival). Suppose that each day the amount of time inminutes that they are late follows an exponential distribution with mean 5.a) Find the probability that they will pay more that 6 dollars in late fees in a given day.b) Assume that in their busy period, they are always at least 4 minutes late. Find the probability thatthey will pay more that 6 dollars in late fees in a given day of busy period. (Hint: Calculate theprobability that they will be late more than 6 minutes given that they are late more than 4 minutes.c) The late fees were no effective in getting this parent to arrive on time, so the daycare change the rateto X? + X dollars for X minutes of tardiness. On average, how much will they pay in late fees eachnormal day. (Hint: You may use mean and variance of exponential distribution, and properties ofexpectation to obtain E[X² + X] .)

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The grade scored by Mehmet in a course is normally distributed with a mean of 50 and standard
deviation of 4.
a) If the probability that Mehmet will pass from this course is 0.8413, what is the passing grade? (Note
that to pass from a score, a student should score a grade which is higher than the passing grade.)
b) The grade scored by another student from the same course is again normally distributed with a mean
of 56 and standard deviation of 3. Find the probability that this student will score higher grade than
Mehmet.

A parent has their child in daycare twice a week. Being busy people they are often a few minutes late
to pick her up. The daycare has a strict policy that parents need to be on time. They enforce this by
charging 1 dollar per minute for tardiness (late arrival). Suppose that each day the amount of time in
minutes that they are late follows an exponential distribution with mean 5.
a) Find the probability that they will pay more that 6 dollars in late fees in a given day.
b) Assume that in their busy period, they are always at least 4 minutes late. Find the probability that
they will pay more that 6 dollars in late fees in a given day of busy period. (Hint: Calculate the
probability that they will be late more than 6 minutes given that they are late more than 4 minutes.
c) The late fees were no effective in getting this parent to arrive on time, so the daycare change the rate
to X? + X dollars for X minutes of tardiness. On average, how much will they pay in late fees each
normal day. (Hint: You may use mean and variance of exponential distribution, and properties of
expectation to obtain E[X² + X] .)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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