Question

The letter​ "t" makes up an estimated 10​% of a certain language. Assume this is still correct. A random sample of 1200 letters is taken from a randomly​ selected, large book and the​ t's are counted. Find the approximate probability that the random sample of 1200 letters will contain 8.8​% or fewer​ t's.

P( p̂ ≤ 0.088)=____________ (round to three decimal places as needed)

Answer 1

Solution

Given that,

$\sigma$_{$\hat p$} =  $\sqrt$[p ( 1 - p ) / n] =  $\sqrt$ [(0.1 * 0.9) / 1200 ] = 0.0087

P( $\hat p$ $\leq$ 0.088) =

= P[( $\hat p$ - $\mu$ _{$\hat p$} ) / $\sigma$ _{$\hat p$}$\leq$ (0.088 - 0.1) / 0.0087]

= P(z $\leq$ -1.38)

= 0.084

P( $\hat p$ $\leq$ 0.088) = 0.084