Math 301 - Assignment 8
Normal Distribution
Below problems are in addition to the problems that we discussed in the class
.
1.
What is Normal Distribution? Why it is also called “Bell Curve”? Describe the properties of
normal curve.
2.
Find the value of z if the area under a standard normal curve
(a) to the right of z is 0.3622;
(b) to the left of z is 0.1131;
(c) between 0 and z, with z > 0, is 0.4838;
(d) between −z and z, with z > 0, is 0.9500
3.
Given a normal distribution with μ = 30 and σ = 6, find
(a) the normal curve area to the right of x = 17;
(b) the normal curve area to the left of x = 22;
(c) the normal curve area between x = 32 and x = 41;
(d) the value of x that has 80% of the normal curve area to the left;
(e) the two values of x that contain the middle 75% of the normal curve area.
4.
Given a random variable X having a normal distribution with μ = 50 and σ = 10, find the
probability that X assumes a value between 40 and 70.
5.
The heights of 1000 students are normally distributed with a mean of 174.5 centimeters and a
standard deviation of 6.9 centimeters. Assuming that the heights are recorded to the nearest

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- Fall '18
- Normal Distribution, Standard Deviation