Quiz #5 (Ch7) instructions I help Save& Exit Submit Question 3 (of 10) Time rema
ID: 3049094 • Letter: Q
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Quiz #5 (Ch7) instructions I help Save& Exit Submit Question 3 (of 10) Time remalning: 1:44:23 2.00 points Section Exercise 7-56 The Johnson family uses a propane gas grill for cooking outdoors. During the summer they need to replace their tank on average every 32 days. At a randomly chosen moment, determine the following: (a) What is the probability that they can grill out at least 35 days before they need to replace their tank? Round your answer to 4 decimal places.) Probability (b) What is the probability that they can grill out no more than 20 days? (Round your answer to 4 decimal places.) Probability References eBook & Resources Section Exercise 7-56Explanation / Answer
POSSION DISTRIBUTION
pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.
x = is the number of independent trials
I.
mean =
= 32
a.
P( X < 35) = P(X=34) + P(X=33) + P(X=32) + P(X=31) + P(X=30) + P(X=29) + P(X=28) + P(X=27) + P(X=26) + P(X=25) + ....P(X=1)+P(X=0)
= e^-32 * 0 ^ 34 / 34! + e^-32 * ^ 33 / 33! + e^-32 * ^ 32 / 32! + e^-32 * ^ 31 / 31! + e^-32 * ^ 30 / 30! + e^-32 * ^ 29 / 29! + e^-32 * ^ 28 / 28! + e^-32 * ^ 27 / 27! + e^-32 * ^ 26 / 26! + e^-32 * ^ 25 / 25! + .... + e^-32 * 0 ^ 1 / 1! + e^-32 * ^ 0 / 0!
= 0.67923
P( X > = 35 ) = 1 - P (X < 35) = 0.3208
b.
P( X < = 20) = P(X=20) + P(X=19) + P(X=18) + P(X=17) + P(X=16) + P(X=15) + P(X=14) + P(X=13) + P(X=12) + P(X=11) + P(X=10) + ....+ ....P(X=1)+P(X=0)
= e^-32 * 32 ^ 20 / 20! + e^-32 * 0 ^ 19 / 19! + e^-32 * ^ 18 / 18! + e^-32 * ^ 17 / 17! + e^-32 * ^ 16 / 16! + e^-32 * ^ 15 / 15! + e^-32 * ^ 14 / 14! + e^-32 * ^ 13 / 13! + e^-32 * ^ 12 / 12! + + e^-32 * 0 ^ 1 / 1! + e^-32 * ^ 0 / 0!
e^-32 * ^ 11 / 11! + e^-32 * ^ 10 / 10! + = 0.0159
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