SOLUTION: The time it takes Jessica to bicycle to school is normally distributed, with a mean time of 15 minutes and a variance of 4 minutes. Jessica has to be at school at 8:00am. What time

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Question 1168121: The time it takes Jessica to bicycle to school is normally distributed, with a mean time of 15 minutes and a variance of 4 minutes. Jessica has to be at school at 8:00am. What time should she leave her house so she will be late only 4% of the time?
Found 2 solutions by VFBundy, Theo:
Answer by VFBundy(438) (Show Source):
You can put this solution on YOUR website!
= 1.75 (from z-table)

x - 15 = 4(1.75)

x - 15 = 7

x = 22

If Jessica leaves her house by 7:38 AM (22 minutes before 8:00 AM), she will be late only 4% of the time.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the mean is 15 minutes.
the variance is 4 minutes.
standard deviation = sqrt(variance) = sqrt(4) = 2

use an online calculator such as the one found at http://davidmlane.com/hyperstat/z_table.html

select value from an area.
set area to .04
set mean to 15
set standard deviation to 2.
select above.

calculator says 18.501 minutes to get to school is exceeded only 4% of the time.

confirm by doing the following:

select area from a value
set mean to 15
set standard deviation to 2
select above
enter 18.501 into above
hit return

calculator says 18.501 minutes to get to school is exceeded only 4% of the time.

what this says is that if she leaves 18.501 minutes before 8:00 am, she will be on time 96% of the time and she will be late 4% of the time.

that's because the trip takes more than 18.501 minutes only 4% of the time.

18.501 minutes is equal to 18 minutes and 30.06 seconds.

to find out when she needs to leave home, subtract 0:18:30.06 from 8:00:00.

you will get 7:41:29.94.

that's when she has to leave home so that she late only 4% of the time.

8:00:00 minus 7:41:29.94 = 7:59:60 minus 7:41:29.94 resulting in 00:18:30.06.

00:18:30.06 is equal to 18.501 minutes.

you divide the 30.06 seconds by 60 to get .501 minutes.

you add it to 18 minutes to get 18.501 minutes.

here's the displays of the results using the online calculator.

first display is value from an area.

second display is area from a value.

obviously, getting her to leave her house at 7:41:29.94 am is highly unrealistic.

she would probably want to leave her house at 7:40 am.

that would give her 20 minutes to get to school and she would only be late less than 1% of the time (the calculator says .62% of the time).

here's a display of 20 minutes to get to school.

you solution, without rounding, is that she needs to leave her home by 7:41:29.94 am.