Kindly Show the Calculation Typed or on Excel Megastat Q.2.) In the past few Yea

Question

Kindly Show the Calculation Typed or on Excel Megastat

Q.2.) In the past few Years, out sourcing overseas has become more frequently used than ever before by U S companies. However, out sourcing is not without problems. A recent survey by purchasing indicates that 20% of the companies that outsource overseas use consultant. Suppose 15 companies that outsource overseas are randomly selected.

What is the probability that exactly five companies that outsource overseas use a consultant?

What is the probability that more than ten companies that outsource overseas use a consultant?

What is the probability that none of the companies that outsource overseas use a consultant?

What is the probability that between four and eight (inclusive) companies that outsource overseas use a consultant?

Explanation / Answer

Let X be the random variable that companies that outsource overseas use a consultant.

X ~ Binomial(n=15, p=0.2)

What is the probability that exactly five companies that outsource overseas use a consultant?

That is here we have to find P(X=5).

This probability we can find by using EXCEL.

syntax is,

=BINOMDIST(number_s, trials, probability_s, cumulative)

Number_s   is the number of successes in trials.

Trials   is the number of independent trials.

Probability_s   is the probability of success on each trial.

Cumulative   is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.

P(X=5) = 0.1032

What is the probability that more than ten companies that outsource overseas use a consultant?

That is here we have to find P(X > 10).

P(X > 10) = P(X=11) + P(X=12) + P(X=13) + P(X=14) + P(X=15)   

P(X > 10) =  0.000012

What is the probability that none of the companies that outsource overseas use a consultant?

That is here we have to find P(X=0).

P(X=0) = 0.0352

What is the probability that between four and eight (inclusive) companies that outsource overseas use a consultant?

That is here we have to find P(4 < X < 8).

P(4 < X < 8) = P(X=5) + P(X=6) + P(X=7)

= 0.1032 + 0.0430 + 0.0138

= 0.1600

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