Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.

a.Select the probability density function.

1.

2.

3.

4.

Select

b.What is the probability of generating a random number between 0.15 and 0.75 (to 1 decimals)?

c.What is the probability of generating a random number with a value less than or equal to 0.4 (to 1 decimals)?

d.What is the probability of generating a random number with a value greater than 0.7 (to 1 decimals)?

e. Using 50 random numbers given below, compute the mean and standard deviation.

0.651355 0.212909 0.781318 0.790967 0.690221

0.968009 0.866650 0.469499 0.531014 0.783254

0.038784 0.501918 0.167941 0.481035 0.979015

0.700128 0.326172 0.378140 0.291835 0.519313

0.064050 0.678114 0.946099 0.627599 0.075532

0.615055 0.927868 0.564377 0.118947 0.534202

0.314635 0.825017 0.082784 0.721806 0.215795

0.103257 0.818854 0.202941 0.279350 0.092991

0.022661 0.914168 0.754914 0.208632 0.119111

0.630115 0.426045 0.814536 0.328540 0.769279

Mean =

(to 6 decimals)

Standard deviation =

(to 6 decimals)