Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of

Question

Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 5.9 telephone orders per hour. (a) Find the probability that at least 27 minutes will elapse before the next telephone order. (Round intermediate values and your final answer to 4 decimal places.) Probability (b) Find the probability that less than 16 minutes will elapse. (Round intermediate values and your final answer to 4 decimal places.) Probability (c) Find the probability that between 16 and 27 minutes will elapse. (Round intermediate values and your final answer to 4 decimal places.) Probability

Explanation / Answer

Solution:-

= 5.9

a) The probability that at least 27 minutes will elapse before the next telephone order is 0.0703.

Average number of orders in 27 minutes = (5.9/60) × 27

Average number of orders in 27 minutes = = 2.655

Applying poissons distribution formula:-

P(x; ) = (e-) (x) / x!

P(x = 0) = 0.0703

b) The probability that less than 16 minutes will elapse is 0.1344.

Average number of orders in 16 minutes = (5.9/60) × 16

Average number of orders in 16 minutes = = 1.573

Applying poissons distribution formula:-

P(x; ) = (e-) (x) / x!

P(x = 1) = 0.1344

c) The probability that between 16 and 27 minutes will elapse is 0.0522.

Applying poissons distribution formula:-

P(x; ) = (e-) (x) / x!

P(x = 1) at 16 = 0.1344

P(x = 1) at 27 = 0.1866

P(16 < x < 27) = 0.1866 - 0.1344

P(16 < x < 27) =0.0522

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