Childrens attitude towards reading In the journal Knowledge

Children\'s attitude towards reading. In the journal Knowledge Quest (January/February 2002), education professors at the University of Southern California investigated children\'s attitudes toward reading. One study measured third through sixth graders\' attitudes toward recreational reading on a 140-point scale (where higher scores indicate a more positive attitude). The mean score for this population of children was 106 points, with a standard deviation of 16.4 points. Consider a random sample of 36 children from this population, and let x represent the mean recreational reading attitude score for the sample.

(Give answers to 4 decimal places.)

a) What is _x?  

b) What is _x?  

c) Find the z-score for the value x = 100 points.  

d) Find P(x < 100).  

PLEASE HELP!!

Solution

a) What is x?

It is the same as the population mean.

Answer: 106

b) What is x?

As

x = /sqrt(n)

Then

x = 16.4/sqrt(36) = 2.733333333 [answer]

c) Find the z-score for the value x = 100 points.

As

z = (x - ux)*sqrt(n)/x

Then

z = (100-106)*sqrt(36)/16.4 = -2.195121951 [answer]

d) Find P(x < 100).

Using table or technology to get the left tailed area of z = -2.195121951,

P(x<100) = 0.014077425 [answer]