In: Statistics and Probability
The letter "t" makes up an estimated 9% of a certain language. Assume this is still correct. A random sample of 500 letters is taken from a randomly selected, large book and the t's are counted. Find the approximate probability that the random sample of 500 letters will contain 8.3% or fewer t's.
Solution
Given that,
p = 0.09
1 - p = 1 - 0.09 = 0.91
n = 500
= p = 0.09
= p ( 1 - p ) / n
= (0.09 * 0.91) / 500 = 0.0128
P( 0.083) =
= P(( - ) / (0.083 - 0.09) / 0.0128)
= P(z -0.5469)
= 0.2922
Probability = 0.2922