Question

For a certain online store, the distribution of number per hour is approximately normal with mean 1200 purchases and standard deviation 200 purchases. for what proportion of hours will the number of purchases at the online store exceed 1400?
a)5%
b)68%
c)16%
d)32%​

Answer 1

Answer: 16%

Step-by-step explanation:

When we have a normal distribution, the 100% of our sample will be placed in a "gaussian bell".

Where the middle of this bell coincides with the mean.

The mean, in this case, is 1200, and the standard deviation is 200.

In the image below you can see that between the points.

Mean + standard deviation and the end of the graph, we have:

13.5% + 2.35% + 0.15% = 16%

And particularly, if we want to know the percentage that exceed 1400, will be the same percentage above the mean plus the standard deviation.

mean = 1200

SD = 200

mean + standard deviation = 1200 + 200 = 1400.

Then the percentage that exceeds 1400 is equal to the percentage that we found above, then the correct option is C: 16%