nnect MATH 1342 MW 2:00PM Fall 2017 Sec 3 Elementary StatisticS: A Step-By-Step

Question

nnect MATH 1342 MW 2:00PM Fall 2017 Sec 3 Elementary StatisticS: A Step-By-Step MATH Hosted by ALEKS Corp 6.3 Homework Previous 1 2 3 4 5 6 Next Question 1 of 6 (1 point) 6.3 Section Exercise 8 (cal A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 38 families will be between 18 and 20 pounds. Assume that the sample is taken from a large population and the correcetion factor can be ignored. Use a graphing ealculator and round the answer to four decimal places Source: Michael D. Shook and Robert L. Shook, The Book orodds. Su

Explanation / Answer

Here we have given n=38 , s=2.5 , x bar=17.2

given   = 17.2 ,  n= 38, = 2.5

Suppose random samples of size n are drawn from a population with mean and standard deviation .

Then mean of sample mean( x bar) = x = = 17.2

stanard devaition of sample mean ( x bar) = x =   / sqrt(n) = 2.5 / sqrt(38) = 0.4055

Find the probability that x-bar is between 18 and 20 i.e P( 18 < X bar < 20)

  P( 18 < X bar < 20) = P( X bar < 20) -  P( X bar < 18)

=  P( Z < (20-17.2)/0.4055 ) -  P( Z < - (18 -17.2)/0.4055)

=   P( Z < 6.905) -  P( Z < 1.972) = 1-  0.975745 = 0.024255

By using Excel command

Type in empty excel cell

=NORMSDIST(6.905) that will give   P( Z < 6.905) =1 , in same way   P( Z < 1.972) = 0.975745

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