Question

Draw the pic

1. The probability that a customer will purchase today’s special, the “Never Been Feta” burger, is 0.27. Given that 9 customers are currently in line waiting to order, respond to the following:

a) What is the probability that exactly 5 specials will be sold to this set of customers?

         b) Determine the expected number of specials that will be sold.

            c) Calculate the standard deviation for this probability distribution.

2) It is known that at major sporting events only 60% of persons that use the washroom during a break in the action will wash their hands. Assuming that you had observed 14 people leave the washroom, answer the following:

a) The probability that exactly 4 of these people have washed their hands.

b) The probability that more than 10 of these people have washed their hands.

c) The probability that at least 4 of these people will have washed their hands.

d) The expected value for this probability distribution.

3) Based on years of historical data, the salary research firm, HR Pufnstuf, states that the annual salary for a Marketing Manager working on Living Island follows a normal distribution with a mean of $62,000 and a standard deviation of $8,000. Given this information determine the following:

1. The probability that a randomly selected Marketing Manager on Living Island would earn an annual salary of more than $65,000.

       b) The probability that a Living Island Marketing Manager’s annual salary would be between $60,000 and $75,000.

3. The percent of Marketing Manager’s on Living Island with an annual salary of less than $80,000.

4. The probability that any given Marketing Manager’s annual salary on Living Island would be between $75,000 and $85,000.
5. The 95th percentile, i.e. annual salary above which 5% of the Living Island’s Marketing Manager’s would earn.

4) It is known that the average age of major league baseball players is 28.3 years with a population standard deviation of 2.8 years. Determine the probability that the average age of 36 randomly selected National League baseball players is less than 27 years of age?

Answer 1

1)

it is a binomial probability distribution,  
  
and probability is given by  

P(X=x) = C(n,x)*px*(1-p)(n-x)

Sample size , n =    9
Probability of an event of interest, p =   0.27

a)

P ( X =    5   ) = C(   9   ,   5   )*   0.27   ^   5   *   0.73   ^   4
P(X=5)=0.0513

b)

expected Mean = np =    2.43
c)

Variance = np(1-p) =    1.7739
Standard deviation = √variance =    1.3319

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2)

Sample size , n =    14
Probability of an event of interest, p =   0.60

P(X=x) = C(n,x)*px*(1-p)(n-x)

a)

P ( X =    4   ) = C(   14   ,   4   )*   0.60   ^   4   *   0.40   ^   10 = 0.0136(answer)

b)

P(X>10) = ΣC(n,x)*p^x*(1-p)^(n-x) where x goes from 11 to 14

P(X>10)=0.1243

c)

P(X≥4) = 1 - P(X<4) = 1 - ΣC(n,x)*p^x*(1-p)^(n-x) where x goes from 0 to 3

=1-0.0039 = 0.9961(answer)

d)

expected value=np=14*0.60=8.4

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