Question

The typical computer random number generator yields numbers from a uniform distribution of values between 0 and 1, with a mean of 0.500 and a standard deviation of 0.289. If random numbers are generated, find the probability that their mean is between 0.6 and 0.7.

Answer 1

Solution:

We are given that the random variable follows uniform distribution.

a = 0

b = 1

µ = 0.500

σ = 0.289

We have to find P(0.6<Xbar<0.7)

P(0.6<Xbar<0.7) = P(Xbar<0.7) – P(Xbar<0.6)

Find P(Xbar<0.7)

Z = (Xbar - µ)/σ

Z = (0.7 - 0.5)/0.289

Z = 0.692042

P(Z<0.692042) = P(Xbar<0.7) = 0.755544

(by using z-table)

Now find P(Xbar<0.6)

Z = (0.6 - 0.5)/0.289

Z = 0.346021

P(Z<0.346021) = P(Xbar<0.6) = 0.635336

(by using z-table)

P(0.6<Xbar<0.7) = P(Xbar<0.7) – P(Xbar<0.6)

P(0.6<Xbar<0.7) = 0.755544 - 0.635336

P(0.6<Xbar<0.7) = 0.120208

Required probability = 0.120208