A recent study reported that 73% of Americans could only converse in one language. A random sample of 130 Americans was randomly selected. What is the probability that 100 or fewer of these Americans could only converse in one language?

Probability that 100 or fewer of these Americans could only converse in one language is 0.8599.

Step-by-step explanation:

We are given that a recent study reported that 73% of Americans could only converse in one language.

A random sample of 130 Americans was randomly selected.

Let = sample proportion of Americans who could only converse in one language.

The z score probability distribution for sample proportion is given by;

                                 Z  =    ~ N(0,1)

where, p = population proportion of Americans who could only converse in one language = 73%

            = sample proportion = = 0.77

           n = sample of Americans = 130

Now, probability that 100 or fewer of these Americans could only converse in one language is given by = P( 0.77)

      P( 0.77) = P( ) = P(Z 1.08) = 0.8599                    

The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.

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step-by-step explanation:

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