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%

miracrown · Answer

Have you studied the Empirical Rule?

anonymous · Answer

why

miracrown · Answer

We're given  X~ N(27,3) the given info
oh, just to summarize the given info!

anonymous · Answer

I don't understand

miracrown · Answer

I always begin Normal distribution problems that way
just to highlight the parameters
mu and sigma, so now do we know the Empirical Rule?

anonymous · Answer

yes

anonymous · Answer

more?

miracrown · 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.

miracrown · Answer

Have you ever seen that before?

anonymous · Answer

yes

miracrown · Answer

ok so we have to figure out how many standard deviations that given interval is from the mean

miracrown · Answer

the given interval is [24,30]

miracrown · Answer

so how many standard deviations are those 2 values from the mean, which is 27?

anonymous · Answer

3?

miracrown · Answer

well 1 std dev = 3
so those values are 3 units away from the mean, right?
and 1 std dev = 3 units

anonymous · Answer

right

miracrown · Answer

is it easier if I gave you a formula for this?

miracrown · Answer

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?

anonymous · Answer

1 duh

miracrown · Answer

Yes!

miracrown · Answer

So that interval is considered "within 1 standard deviation of the mean"..ok?

miracrown · Answer

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.

anonymous · Answer

Im sorry but are you mad I cant tell

miracrown · Answer

Why are you asking this?

miracrown · Answer

back to the question, any guess, which is the correct percent?

anonymous · Answer

because all the ! marks

miracrown · Answer

lol, its because I'm used to putting the exclamation '!" marks!

anonymous · Answer

is the answer 99.7% ?

miracrown · Answer

within the first std dev is the same as within 1 std dev
68% will fall within the first standard deviation
ok?

miracrown · Answer

Any questions on how I got that result?

anonymous · Answer

so the answer is what? sorry

miracrown · Answer

that would be [27-3(3), 27+3(3)]
within 3 std deviations
this is within 1 standard deviation of the mean

miracrown · Answer

if the given interval was [18, 36] then it would be 99.7%

miracrown · Answer

so the answer should be 68%

anonymous · Answer

thank you do you mind helping with a few more?

miracrown · Answer

I've gotta run, sorry but if you post a new thread then someone else will surely help you out!