The popping-times of the kernels in a certain brand of microwave popcorn are normally distributed with a mean of 150 seconds and a standard deviation of 11 seconds.

The first kernel pops 126 seconds after the microwave oven is started. What is the z-score of this kernel?

Also what in the world is a z-score?

Question

The popping-times of the kernels in a certain brand of microwave popcorn are normally distributed with a mean of 150 seconds and a standard deviation of 11 seconds.

The first kernel pops 126 seconds after the microwave oven is started. What is the z-score of this kernel?

Also what in the world is a z-score?

amistre64 · Answer

a zscore is a standardization of a normal distribution to fit the normal distribution curve with a mean of 0 and a stadard deviation of 1

amistre64 · Answer

in order to move your distribution to a mean of zero, you have to subtract the mean from all the data points .....  x - mean.   Which is rather obvious since: mean - mean = 0

amistre64 · Answer

the next step in the process is to determine a unit value for the standard deviation;  we have to squeeze 11 units into an equivalent 1 unit

amistre64 · Answer

11/11 = 1  works, so for every 11 units from the mean, you equate to 1 standardized unit

amistre64 · Answer

$$z=\frac{x-\bar x}{sd}$$

amistre64 · Answer

how many units of 11, can you squeeze between 150 and 126?

$$z=\frac{126-150}{11}$$

anonymous · Answer

-2.18?

amistre64 · Answer

correct

anonymous · Answer

Thank you very much.

amistre64 · Answer

youre welcome