Question

In: Statistics and Probability

The letter "t" makes up an estimated 9% of a certain language. Assume this is still...

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.

Solutions

Expert Solution

Solution

Given that,

p = 0.09

1 - p = 1 - 0.09 = 0.91

n = 500

= p = 0.09

= $\sqrt$ p ( 1 - p ) / n

= $\sqrt$ (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

orchestra answered 1 year ago

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