Question

Taxi Fares are normally distributed with a mean fare of $22.27 and a standard deviation of $2.20.

(A) Which should have the greater probability of falling between $21 & $24;
the mean of a random sample of 10 taxi fares or the amount of a single random taxi fare? Why?
(B) Which should have a greater probability of being over $24-the mean of 10 randomly selected taxi fares or the amount of a single randomly selected taxi fare? Why?

Answer 1

Explanation:

Given that taxi Fares are normally distributed with a mean fare of $22.27 and a standard deviation of $2.20.

For a random single taxi std deviation is 2.20

But for a sample of size 10, std deviation would be

`(2.20)/(√(10) )`

This would be less than the 2.20

Because std devition is less for sample we get a big z score for the sample than the single.

As positive values of z increase we find that probability would decrease since normal curve is bell shaped.

So single taxi fare would have higher probability than sample.

B) Here >24.

By the same argument we have z value less for single taxi hence the probability for more than that would be less than that of sample size 10