Question

A recent study reported that 51​% of the children in a particular community were overweight or obese. Suppose a random sample of 500 public school children is taken from this community. Assume the sample was taken in such a way that the conditions for using the Central Limit Theorem are met. We are interested in finding the probability that the proportion of​ overweight/obese children in the sample will be greater than 0.47. Complete parts​ (a) and​ (b) below. . Calculate the probability that 47​% or more of the sample are overweight or obese.

Answer 1

Solution:

Given that,

n = 487

= 51% =0.51

1 - = 1 - 0.51 = 093

=   = 0.07

= ( 1 - ) / n

=  0.51 * 0.49 / 500

= 0.0223

= 0.0223

p (   > 0.47 )

= 1 -  p (   < 0.47 )

= 1 - p ( -    / ) < ( 0.47 - 0.51 / 0.0223 )

= 1 - p ( z < -0.01 / 0.0223 )

= 1 - p ( z < -1.79)

Using z table

= 1 - 0.0367

= 0.9633

Probability = 0.9633