Question

Suppose a simple random sample of size n= 150 is obtained from a population whose size is N=15,000 and whose population proportion with a specified characteristicis p=02 bts Click here to view the standard normal distribution table (page 11 Click here to view the standard normal distribution table (page 2) HA=02 (Round to one decimal place as needed) Determine the standard deviation of the sampling distribution of GA 0.326599 (Round to six decimal places as needed) Pulm (b) What is the probability of obtaining x 39 or more individuals with the characteristic? That is what is PP20 26) Pip20.26)- Round to four decimal places as needed) (c) What is the probability of obtaining x = 24 or fewer individuals with the characteristic? That PI 016)- Round to four decimal places as needed) PPS 152

Answer 1

Solution

Given that,

$\mu$$\hat p$ = 0.2

$\sigma$$\hat p$ =  $\sqrt$[p( 1 - p ) / n] = $\sqrt$ [(0.2 * 0.8) / 150 ] = 0.032660

b) P( $\hat p$   $\geq$ 0.26) = 1 - P( $\hat p$ $\leq$ 0.26 )

= 1 - P(( $\hat p$ - $\mu$ $\hat p$ ) / $\sigma$ $\hat p$  $\leq$ (0.26 - 0.2) / 0.032660 )

= 1 - P(z $\leq$ 1.84)

= 1 - 0.9671

= 0.0329

c) P( $\hat p$ $\leq$ 0.16)

= P[( $\hat p$ - $\mu$ $\hat p$ ) / $\sigma$ $\hat p$$\leq$ (0.16 - 0.2) / 0.032660 ]

= P(z $\leq$ -1.22)

Using z table,

= 0.1112