Rmarkdown A study of stress on among the students in a college campus shows that

Question

Rmarkdown

A study of stress on among the students in a college campus shows that the stress scores follow a Uniform distribution with the lowest stress score equal to 1 and the highest equal to 5. Use a sample of 75 students and those four (d, p, q, r) built-in R functions for the probability distribution of random variable to compute the following (a) The probability that the average stress score for the 75 students is less than 2. (b) The 90th percentile for the average stress score for the 75 students. (c) The probability that the total of the 75 stress scores is less than 200. (d) The 90th percentile for the total stress score for the 75 students.

Explanation / Answer

here mean for uniform distribution=(a+b)/2 =(1+5)/2=3

and std deviation =(b-a)/(12)1/2 =1.1547

hence mean for 75 students =3

and std error of mean =1.1547/(75)1/2 =0.13333

hence P(X<2)=P(Z<(2-3)/0.13333)=P(Z<-7.5)=0.0000

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