Assignment8_NormalDistribution.docx - Math 301 Assignment 8 Normal Distribution Below problems are in addition to the problems that we discussed in the

Assignment8_NormalDistribution.docx - Math 301 Assignment 8...

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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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