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the letter "T" makes up an estimated 8% of a certain language. Assume this still correct. A random sample of 1000 letters is taken from a randomly selected, large book and the t's are counted. find the approximate probability that the random sample of 1000 letters will contain 7.4% or fewer t's​

Answer :

MathPhys

Answer:

0.242

Step-by-step explanation:

p = 0.08, q = 1 − p = 0.92, and n = 1000.

The mean and standard deviation are:

μ = p = 0.08

σ = √(pq/n) = 0.00858

The z score is:

z = (x − μ) / σ = -0.70

Using a calculator or z score table, the probability is:

P(Z < -0.70) = 0.242

The approximate probability that the random sample of 1000 letters will contain 7.4% or fewer is; 0.242

What is the probability?

We are given;

proportion; p = 0.08

n = 1000.

Thus; q = 1 − p = 0.92

The  is equal to the proportion. Thus;

μ = p = 0.08

Formula for the standard deviation is;

σ = √(pq/n)

σ = 0.00858

The z score is gotten from the formula;

z = (x − μ)/σ

z = (0.074 -0.08)/0.00858

z = -0.70

From online p-value from z-score calculator, we have;

P(Z < -0.70) = 0.242

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