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Suppose the mean income of firms in the industry for a year is 95 million dollars with a standard deviation of 11 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 114 million dollars

Respuesta :

Manetho

Answer:

95.73%

Step-by-step explanation:

Given data:

mean μ= 95

standard deviation, σ = 11

to calculate, the probability that a randomly selected firm will earn less than 114 million dollars;

Use normal distribution formula

[tex]P(X<114)=P(Z<\frac{X-\mu}{\sigma} )[/tex]

Substitute the required values in the above equation;

[tex]P(X<114)=P(Z<\frac{114-95}{11} )\\P(X<114)=P(Z<1.7272)\\P(X<114)=0.9573[/tex]

Therefore, the probability that a randomly selected firm will earn less than 114 million dollars = 95.73%

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