In the production of chocolate chip cookies, one can consider each cookie to be
ID: 3065705 • Letter: I
Question
In the production of chocolate chip cookies, one can consider each cookie to be the specified interval unit required for a Poisson distribution, and one can consider the variable x to be the number of chocolate chips in a cookie. The data set below includes the numbers of chocolate chips in 34 different chocolate chip cookies. The Poisson distribution requires a value for , so use 30.8, which is the mean number of chocolate chips in the 34 cookies. Assume that the Poisson distribution applies. Complete parts a and b below (round to the nearest three decimals)
a).Find the probability that a cookie will have 26 chocolate chips, then find the expected number of cookies with 26 chocolate chips among 34 different cookies, then compare the result to the actual number of cookies with 26 chocolate chips Consider the expected value to be close to the actual value if the absolute value of their difference is less than
1. How does this result compare to the actual number of cookies with 26 chocolate chips
B). Find the probability that a cookie will have 26 chocolate chips, then find the expected number of cookies with 26 chocolate chips among 34 different cookies, then compare the result to the actual number of cookies with 30 chocolate chips.
1. How does this result compare to the actual number of cookies with 30 chocolate chips
27
38
23
40
33
22
32
30
36
28
36
38
27
27
31
35
32
29
27
40
23
34
33
26
30
35
27
28
37
35
29
27
23
30
a).Find the probability that a cookie will have 26 chocolate chips, then find the expected number of cookies with 26 chocolate chips among 34 different cookies, then compare the result to the actual number of cookies with 26 chocolate chips Consider the expected value to be close to the actual value if the absolute value of their difference is less than
1. How does this result compare to the actual number of cookies with 26 chocolate chips
B). Find the probability that a cookie will have 26 chocolate chips, then find the expected number of cookies with 26 chocolate chips among 34 different cookies, then compare the result to the actual number of cookies with 30 chocolate chips.
1. How does this result compare to the actual number of cookies with 30 chocolate chips
27
38
23
40
33
22
32
30
36
28
36
38
27
27
31
35
32
29
27
40
23
34
33
26
30
35
27
28
37
35
29
27
23
30
Explanation / Answer
Probability that a cookie will have 26 chocolate chips
= P(x = 26) = exp(-30.8) (30.826) / 26! = 0.0525
Expected number of cookies with 26 chocolate chips among 34 different cookies = 34 * 0.0525 = 1.785
Actual number of cookies with 26 chocolate chips in given data = 1
Absolute value of their difference = 1.785 - 1 = 0.785 which is less than 1.
So, the expected value to be close to the actual value.
B)
From part (A),
Expected number of cookies with 26 chocolate chips among 34 different cookies = 1.785
Actual number of cookies with 26 chocolate chips in 1st 30 chocolate chips = 1
Absolute value of their difference = 1.785 - 1 = 0.785 which is less than 1.
So, the expected value to be close to the actual value.
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