Question

. For a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20. On what percent of the flights would you expect from 340 to 420 pieces of checked luggage?

Answer 1

Answer: We have 95% chances of flight that would be expected from 340 to 420 pieces of checked luggage.

Explanation:

Since we have given that

The number of pieces of checked has mean and standard deviation as follows:

Sample mean (
`\mu` ) = 380

Sample standard deviation (
`\sigma` )= 20

We need to find the percentage of flights would be expected from 340 to 420 pieces of checked luggage.

So, if we take X = 340,

As it is normal distribution,

Then,

`(X-\mu)/(\sigma)\\\\=(340-380)/(20)\\\\=(-40)/(20)\\\\=-2`

Similarly, if we take X = 420 pieces,

`(X-\mu)/(\sigma)\\\\=(420-380)/(20)\\\\=(40)/(20)\\\\=2`

so, there are 2 standard deviations above the mean and 2 standard deviations below the mean.

So, in this case, we have 95% chances of flight that would be expected from 340 to 420 pieces of checked luggage.

Answer 2

340 is (340-380)/20=-2, or 2 standard deviations below the mean.
420 is (420-380)/20=2, or 2 standard deviations below the mean.

95% of values lie within 2 standard deviations of the mean, so the answer is 95%.