1) Suppose the given represents the average number of emergency visits at a loca

ID: 3205911 • Letter: 1

Question

1) Suppose the given represents the average number of emergency visits at a local hospital each hour.

a) What is the probability of no calls for 2 hours and 15 minutes?

b) If the hospital receives more than 12 calls in a 4-hour period they will send patients to another hospital. What is the probability this occurs?

2) Suppose X is a negative binomial distribution with the given and r=number of successes.

a) Find the expected number of TRIALS (not failures).

b) What is the probability of ten or less failures before r successes?

3) For the given table find E(X), V(X) and F(X). Show work. Copy and paste from Excel as needed.

1) mu= 1.25 2) pi= 0.3565 r= 7 3) X P(X) 1 0.1786 2 0.0849 3 0.0129 4 0.0258 5 0.1611 6 0.0907 7 0.0764 8 0.1317 9 0.0788 10 0.1591

Result:

1) Suppose the given represents the average number of emergency visits at a local hospital each hour.

a) What is the probability of no calls for 2 hours and 15 minutes?

Average number of emergency visits for 2 hours and 15 minutes = 1.25*2.25 =2.8125

Poisson distribution used.

P( x =0) =0.0601

b) If the hospital receives more than 12 calls in a 4-hour period they will send patients to another hospital. What is the probability this occurs?

Average number of emergency visits for 4 hours = 1.25*4 =5

Poisson distribution used.

P( x >12) = 0.002

2) Suppose X is a negative binomial distribution with the given and r=number of successes.

a) Find the expected number of TRIALS (not failures).

expected number of TRIALS = r/p=7/0.3565=19.6

=20 (rounded)

b) What is the probability of ten or less failures before r successes?

P( x 10) = 0.4032

3) For the given table find E(X), V(X) and F(X). Show work. Copy and paste from Excel as needed.

Expectation = r(1 - p)/p = 12.635343618513

Variance = r(1 - p) / p2 = 35.442759098214

Standard deviation = 5.953382156238

P(X=x) = (r+x-1Cx) pr (1-p)x for x = 0, 1, ...

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