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babas97
29.03.2020 •
Mathematics
In a certain microwave oven on the high power setting, the time it takes a randomly chosen kernel of popcorn to pop is normally distributed with a mean of 140 seconds and a standard deviation of 25 seconds.
A) what percentage of the kernels will fail to pop if the popcorn is cooked for 2 minutes?
B) what percentage of the kernels will fail to pop if the popcorn is cooked for 3 minutes?
C) if you wanted 95% of the kernels to pop, what time would you allow?
D) if you wanted 99% of kernels to pop, what time would you allow?
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Ответ:
A) The percentage of the kernels will fail to pop if the popcorn is cooked for 2 minutes is 78.8%
B) The percentage of the kernels will fail to pop if the popcorn is cooked for 3 minutes is 5.48%
C) For 95% of the kernels to pop, the time to be allowed is 3 minutes and 11.13 seconds
D) For 99% of the kernels to pop, the time to be allowed is 3 minutes and 18.15 seconds
Step-by-step explanation:
A) The percentage of the kernels will fail to pop if the popcorn is cooked for 2 minutes
2 minutes = 120 seconds
z(120) = (120 - 140) / 25
= -20 / 25
= - 0.8
p(z > - 0.8) = 1 - p ( 2 < - 0.8)
= 1 - 0.2119
= 0.7881
= 78.8%
B) The percentage of the kernels will fail to pop if the popcorn is cooked for 3 minutes
3 minutes = 180 seconds
z(120) = (180 - 140) / 25
= 40 / 25
= 1.6
p(z > 1.6) = 1 - p ( 2 < 0.9452)
= 0.0548
= 5.48%
C) For 95% of the kernels to pop, the time to be allowed is
The Z value that gives an area of 0.05 for the right tail > 1.645
From the formula ,
2 (x) = (x -μ ) / r
1.645 = (x - 140) / 25
x - 140 = 1.645 x 25
x - 140 = 41.12
x = 41.13 + 140
x = 181.13
Thus, For 95% of the kernels to pop, the time to be allowed is 3 minutes and 11.13 seconds
D) For 99% of the kernels to pop, the time to be allowed is
The Z value that gives an area of 0.05 for the right tail > 2.326
From the formula ,
2 (x) = (x -μ ) / r
2.326 = (x - 140) / 25
x - 140 = 2.326 x 25
x - 140 = 58.15
x = 58.15 + 140
x = 198.15
Thus, For 99% of the kernels to pop, the time to be allowed is 3 minutes and 18.15 seconds
Ответ:
look to rule number five
Step-by-step explanation:
Rule Number 5 best explains the answer