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Stuck for a formula
Message posted by Michael (via 198.208.6.35) on September 7, 2001 at 12:08 PM (ET)
I'm stuck trying to figure out the formula and application for this problem. Can anyone help? I've done it three different ways and am not confident at al with the outcome. Here it is:
Historically, 93% of our UPS overnite deliveries arrive before 9:00. If we take random samples of 500 deliveries what proportion of the samples will have
(1) Between 93% and 95% of the deliveries arriving before 9:00?
(2) More than 95% of the deliveries arriving before 9:00?
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: Stuck for a formula
Message posted by nancy diehl (via 129.176.151.121) on September 7, 2001 at 1:46 PM (ET)
Here's how I would answer your problem. Basically, what you need to do is figure out what the area under the normal curve represents the area between .93 and .95 where .93 represents the historical mean. I would draw yourself a normal curve, drop a line down the center to represent .93, or the mean, which is np=.93*500=465. Drop a line to represent .95, which is .95*500=475. The area you need to find is between these two lines. You need to translate the value of 475 to a Z-value, then look this up in the Z table to determine the area it represents. So, you know the mean is np=465, the standard deviation is SQRT(n*p*(1-p)) = SQRT(500*.93*.07) = 5.71. Use the formula to find Z: (observ - mean)/stdev. = (475-465)/5.71 = 1.75. Use the Z table to find what 1.75 represents. The area under the normal curve between the mean and 1.75 equals .4599, or 45.99%, which answers your first part. The area beyond 1.75 equals .5-.4599 = .0401 or 4.1% which answers the second question.
Re: Stuck for a formula
Message posted by Michael (via 198.208.6.35) on September 7, 2001 at 2:22 PM (ET)
Thanks, Nancy. I get it all to a point - how did you figure the area under the curve between the mean and 1.75 to be .4599?
Thanks!
Re: Stuck for a formula
Message posted by Joan (via 146.203.102.93) on September 7, 2001 at 2:53 PM (ET)
You find the area by using a stats book with a Z table in the back.
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