A study found that the mean seconds, complete The probability that a randomly se
ID: 3065180 • Letter: A
Question
A study found that the mean seconds, complete The probability that a randomly seolected car will get through the restaurant's drive-through in less than 100 seconds is (Round to four decimal places as needed) more than 200 seconds in the restaurant's drive-through? The probablity that a randomly selected car will spend more than 200 seconds in the restaurant's drive-through is (c) What proportion of cars spend The proportion of cars that spend between 2 and 3 minutes in the restaurant's drive-through is 3 minutes in the restaurant's drive-through? to four decimal places as needed ) han 0.06 Round to four decimal olaces as needed.)Explanation / Answer
X ~ N(141.4 , 322)
By central limit theorem
Z = ( X -141.4)/32 ~ N(0,1)
a) Required probability = P( X < 100)
= P ( (X - 141.4)/32 < (100 -141.4)/32)
= P(Z < -1.2937)
From Normal probability table
P(Z < -1.2937) = 0.0978
The probability that a randomly selected car will go through the restaurant driver-through in less than 100 sec is
0.0978
b ) Required Probability = P ( X >200)
= P ( (X - 141.4)/32 >(200 -141.4)/32)
= P(Z > 1.8312)
From Normal probability table
P(Z >1.8312) = 0.0335
The probability that a randomly selected car will spend more than 200 seconds in the restaurant driver-through is
0.0335
c) Required probability = P ( 2 min < X < 3min)
= P ( X > 2 min) - P (X > 3 min)
= P ( X >120 ) - P( X > 180)
=P ( (X - 141.4)/32 >(120 -141.4)/32) - P ( (X - 141.4)/32 >(180 -141.4)/32)
=P ( Z> -0.6687) - P ( Z > 1.2062)
From normal probability table
P ( Z> -0.6687) = 0.7482 and P ( Z > 1.2062) = 0.1139
P ( 2 min < X < 3min) = 0.7482 - 0.1139 = 0.6343
The propertion of car that spend between 2 and 3 minutes in the restaurant driver through is 0.6343 ( 63.43%)
d) The probability that a car spends more than 3 minutes in the restaurant driver through is 0.1139 ( P (X >3 ) = P(Z > 1.2062) = 0.1139) so it not be unusual since the probability is greater than 0.05
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