Question

In: Statistics and Probability

3. The distances traveled by individuals to work is exponential, with a mean of 9 miles....

3. The distances traveled by individuals to work is exponential, with a mean of 9 miles.

(a) What is the probability that they travel between 5 and 11 miles? (2)

(b) What is the 80^th percentile of this distribution? (2)

4. The annual number of crimes in a city has a normal distribution, with mean 200, and standard deviation 42.

(a) What is the probability of less than 150 crimes next year? (2)

(b) What is the 75^th percentile of this distribution? (2)

Expert Solution

3. The distances traveled by individuals to work is exponential, with a mean of 9 miles.

(a) What is the probability that they travel between 5 and 11 miles?

The provided mean is β=9.

We need to compute . Therefore, the following is obtained:

which completes the calculation.

(b) What is the 80^th percentile of this distribution?

P[ X < x_80 ] = 80% = 0.8

4. The annual number of crimes in a city has a normal distribution, with mean 200, and standard deviation 42.

(a) What is the probability of less than 150 crimes next year?

The following information has been provided:

We need to compute The corresponding z-value needed to be computed:

Therefore,

(b) What is the 75^th percentile of this distribution?

P[ X < x_75 ] = 75% = 0.75

Also, P[ Z < 0.674 ] = 0.75

orchestra answered 2 years ago

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