Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Approximately what percent of pizzas are delivered between 24 and 30 minutes?

32%
68%
95%
99.7%

Question

Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Approximately what percent of pizzas are delivered between 24 and 30 minutes?

 32%
 68%
 95%
 99.7%

anonymous · Answer

@AG23 @nincompoop @horsegirl27 Can you please help me understand how to do these types of problems.?

cbarredo1 · Answer

Have you studied the Empirical Rule?

anonymous · Answer

I have not.

cbarredo1 · Answer

A statistical rule stating that for a normal distribution, almost all data will fall within three standard deviations of the mean. Broken down, the empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean.

cbarredo1 · Answer

ok so we have to figure out how many standard deviations that given interval is from the mean
the given interval is [24,30]
so how many standard deviations are those 2 values from the mean, which is 27?

anonymous · Answer

I'm sorry, but what is a standard deviation.? I Quit school for a few purposes and here i am 3 years later and i just need a refreshing. Isn't that kind of like the mean of a data set.?

cbarredo1 · Answer

well 1 std dev = 3
so those values are 3 units away from the mean, right?
and 1 std dev = 3 units
so we want k here ---     [24, 30] = [27-3k, 27+3k]
so we can solve either of these equations
24 = 27 - 3k
or 
30 = 27 + 3k
so what is K? 
So that interval is considered "within 1 standard deviation of the mean"..ok?
so that's what we use to get our answer from the empirical rule -
A statistical rule stating that for a normal distribution, almost all data will fall within three standard deviations of the mean. Broken down, the empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean. 
within the first std dev is the same as within 1 std dev
68% will fall within the first standard deviation
that would be [27-3(3), 27+3(3)]
within 3 std deviations
this is within 1 standard deviation of the mean
if the given interval was [18, 36] then it would be 99.7%

cbarredo1 · Answer

The answer would be 68%

cbarredo1 · Answer

It is a quantity calculated to indicate the extent of deviation for a group as a whole.

anonymous · Answer

okay sweet thank you (:

cbarredo1 · Answer

Did you get it?

anonymous · Answer

I understand it now.