The random-number generator on your If I calculator yields numbers from a unifor

Question

The random-number generator on your If I calculator yields numbers from a uniform distribution of values between 0 and 1, with mean = 0.500 and standard deviation = 0.289. a) If one value is randomly generated, find the probability that the number is between 0.24 and 0.57. b) If a sample of 126 such numbers are randomly generated, find the probability that the mean of the sample is less than 0.47. c) Would be unusual to randomly generate 126 such numbers and get a sample mean less than 0.47? Why or why not?

Explanation / Answer

as z score =(X-mean)/std deviation

a)P(0.24<X<0.57)=P(-0.8997<Z<0.2422)=0.5957-0.1842=0.4115

b) for n=126 std deviation of mean=0.289/(126)1/2 =0.0257

hence P(X<0.47)=P(Z<-1.1652)=0.1220

c) as probabilty of that is greater then 0.05 level we can not consider that as unusal

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