aIf x is a normal random variable with mean 80 and standard

a.If x is a normal random variable with mean 80 and standard deviation 5, calculate the z score if x=88.

b.Let z be a normal random variable with mean 0 and standard deviation 1. Find P(1.3 < z < 2.3). Sketch the graph, shade the appropriate area in the curve.

c.The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last longer than 1150 hours?

d.The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 1100 hours?

e.Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20. Determine the value of x such that 60% of the values are greater than x.

f.Suppose you are working with a data set that is normally distributed with a mean of 400 and a standard deviation of 20. Determine the value of x such that only 1% of the values are greater than x.

Solution

x -1 0 1 y a) x Mean Sd z 88 80 5 1.6 b) 0 1 1.33) 0.00 d) 1100 1000 50 2 P(Z<2) 0.9772 e) 400.51 400 20 0.0255 x=400.51 f) 446.6 400 20 2.33 x= 446.6