A small café downtown is visited by an average of 18 customers each day. The pro
ID: 3442584 • Letter: A
Question
A small café downtown is visited by an average of 18 customers each day. The probability that a customer orders a cocktail is 0.4400. Use Minitab to calculate probability and cumulative probability tables for the experiment. Format the columns to four decimals. Copy your output and paste it into your MSWord document. Convert the text to a table, and format the output so that the columns are aligned. Then, answer the following questions in your MSWord document.
a. Compute the expected value, E(x)
b. Compute the variance, 2 (x)
c. Compute standard deviation, (x).
d. Eighteen people enter the café …what is the probability that exactly twelve order a cocktail?
e. Eighteen people enter the café …what is the probability that at least twelve order a cocktail?
f. Eighteen people enter the café …what is the probability that fewer than twelve order a cocktail?
g. Eighteen people enter the café …what is the probability that more than six order a cocktail?
h. Eighteen people enter the café …what is the probability that no more than eight order a cocktail?
i. Eighteen people enter the café …what is the probability that fewer than ten or more than sixteen order a cocktail?
j. Eighteen people enter the café …what is the probability that more than seven but fewer than fourteen order a cocktail?
Explanation / Answer
Normal Distribution
a)
Mean ( np ) =7.92
b)
Variacne = npq = 18*0.44*0.56 = 4.4352
c)
Standard Deviation ( npq )= 18*0.44*0.56 = 2.106
d)
P( X = 12 ) = ( 18 12 ) * ( 0.44^12) * ( 1 - 0.44 )^6
= 0.0301
e)
P( X > = 12 ) = P(X=18)+ P(X=17) + P(X=16) + P(X=15) + P(X=14) + P(X=13) + P(X=12) = 0.0449
f)
P(X < 12) = 1 - P( X > = 12 ) = 0.9551
g)
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 18 5 ) * 0.44^5 * ( 1- 0.44 ) ^13 + ( 18 4 ) * 0.44^4 * ( 1- 0.44 ) ^14 + ( 18 3 ) * 0.44^3 * ( 1- 0.44 ) ^15 + ( 18 2 ) * 0.44^2 * ( 1- 0.44 ) ^16 + ( 18 1 ) * 0.44^1 * ( 1- 0.44 ) ^17 + ( 18 0 ) * 0.44^0 * ( 1- 0.44 ) ^18
= 0.1243
P( X > 6) = 1 - P ( X <=6) = 1 -0.2524 = 0.7476
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