A recent issue of Bride Magazine suggested that couples planning their wedding s

Question

A recent issue of Bride Magazine suggested that couples planning their wedding should expect two-thirds of those who are sent an invitation to respond that they will attend. Rich and Stacy are planning to be married later this year. They plan to send 197 invitations.

a.. What is the standard deviation? (Round your answer to 4 decimal places.)

Standard deviation_____

c. What is the probability 140 or more will accept the invitation? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Probability_____

d. What is the probability exactly 140 will accept the invitation? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Probability______

Explanation / Answer

n = 197
p =

a)
= [ (np)(1 - p) ] = [ (197)()() ] = 6.616

c)Binomial distribution but approximate using the normal distribution
z = (x - µ) / = (140 - 131.33333) /6.616 = 1.30986
determine p value from the z-score index table
P(x < 140) = P(z = 1.30986) = 0.904879
P(x 140) = 1 - P(x < 140) = 1 - 0.904879 = 0.095121 = 0.0951

d)Binomial distribution but approximate using the normal distribution
140 is between 139.5 and 140.5
z = (x - µ) / = (140.5 - 131.33333) /6.616 = 1.38553
z = (x - µ) / = (139.5 - 131.33333) /6.616 = 1.23438
P(X = 140) = P(z = 1.38553) - P(z = 1.23438)
P(X = 140) = 0.917055 - 0.891469
P(X = 140) = 0.025586 = 0.026

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