Standard Deviation: A manufacturer finds that the delivery times of a certain item...

[vinnyd53]

**Hi, I cant figure out this question and I need help**


A manufacturer finds that the delivery times of a certain item to customers is normally distributed with a mean of 16 working days and a standard deviation of 2.5 working days. The manufacturer has given customers a guarantee of "delivery within 20 working days " what percentage of customers will receive their deliveries late?


** I don't understand wouldn't it be 0% since its only 2.5 days away from the mean making it 18.5 days? **

 

[Deleted member 4993]

**Hi, I cant figure out this question and I need help**


A manufacturer finds that the delivery times of a certain item to customers is normally distributed with a mean of 16 working days and a standard deviation of 2.5 working days. The manufacturer has given customers a guarantee of "delivery within 20 working days " what percentage of customers will receive their deliveries late?


** I don't understand wouldn't it be 0% since its only 2.5 days away from the mean making it 18.5 days? **

Have you studied z-distribution (transformation)?

 

[Ishuda]

**Hi, I cant figure out this question and I need help**


A manufacturer finds that the delivery times of a certain item to customers is normally distributed with a mean of 16 working days and a standard deviation of 2.5 working days. The manufacturer has given customers a guarantee of "delivery within 20 working days " what percentage of customers will receive their deliveries late?


** I don't understand wouldn't it be 0% since its only 2.5 days away from the mean making it 18.5 days? **

As Subhotosh Khan mentioned, you need to study the concepts behind what is meant by standard deviation and other statistical methods (especially for the Normal Distribution for these type problems).

To start with a standard deviation is not that value away from the mean where all the data lie, just most of it. For the normal distribution, about 34% falls within 1 standard deviation to the right of the mean and about 34% falls within 1 standard deviation to the left of the mean so that about 68% falls within 1 standard deviation of the mean. For within two standard deviations of the mean, about an additional 27% is added to that for a total of about 95% of the data fall within two standard deviations of the mean. etc.