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?

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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have