Assignment 3
Probability & Statistics
29th April, 2022
BMEN, BMMP & BGEN
1. The achievement scores for a college entrance examination are normally distributed with mean
75 and standard deviation 10. What fraction of the scores lies between 80 and 90?
2. If Z is a standard normal random variable, find the value 𝑧0 such that
i.
P(Z > 𝑧0 ) = .5.
ii.
P(Z < 𝑧0 ) = .8643.
3. If a parachutist lands at a random point on a line between markers A and B, find the probability
that she is closer to A than to B. Find the probability that her distance to A is more than three
times her distance to B.
4. The magnitude of earthquakes recorded in a region of North America can be modeled as having
an exponential distribution with mean 2.4, as measured on the Richter scale. Find the
probability that an earthquake striking this region will exceed 3.0 on the Richter scale.
5. State and prove the central limit theorem.
6. The fracture strength of tempered glass averages 14 (measured in thousands of pounds per
square inch) and has standard deviation 2.
i.
What is the probability that the average fracture strength of 100 randomly selected
pieces of this glass exceeds 14.5?
ii.
Find an interval that includes, with probability 0.95, the average fracture strength of
100 randomly selected pieces of this glass.
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Instructions
Form 10 groups.
Each group should have 2 from BMMP, 3 From BMEN and 3 or 4 from BGEN.
Hand in printed.
Due date is 6th of May 2022; 7:40 AM.