Question

A population of values has a normal distribution with ?=64.8 and ?=44.8. You intend to draw a random sample of size n=15.

Find the probability that a single randomly selected value is greater than 76.4.
P(X > 76.4) =

Find the probability that a sample of size n=15 is randomly selected with a mean greater than 76.4.
P(M > 76.4) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Z =X--MEAN/S.D.

Z=76.4-64.8 /44.8=11.6/44.8 =0.2589

Now Z =0.2589,it simply means that X value is greater than 1.2589 times mean

mean here is 64.8 so X=1.258964.8 ,X=81.57672

Now we have to find the probability(X greater than 76.4 or Z reater than 81.5767)

use z table for n=15 to find the rquired probaility

B)Mean greater than 76.4 means

Z=76.4-X/44.8 OR

Z=76.4-76.4/44.8 ,z=0

WE HAVE TO FIND PEOBABILITY WHEN Z LESS THAN ZERO(MEANS NEAGETIVE)

use table for n=15 and Z is less than zero ,probability is find