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 1 year ago

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

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

The following are distances (in miles) traveled to the workplace by 17 employees of a certain...

The following are distances (in miles) traveled to the workplace by 17 employees of a certain hospital. 9, 27, 31, 18, 1, 28, 13, 32, 3, 18, 29, 16, 2, 37, 14, 22, 11 What is The 25th percentile? What is the 70th percentile?

manager wishes to determine the relationship between the number of miles traveled (in hundreds of miles)...

manager wishes to determine the relationship between the number of miles traveled (in hundreds of miles) by her sales representatives and their amount of sales (in thousands of dollars) per month. Complete the linear regression test below in order to predict the amount of sales if the sales representative traveled 1,300 miles? By visual observation of the scatter plot, does the data appear linear? Null Hypothesis: Alternative Hypothesis: What is the value of r? What are the critical values for...

3. The following frequency table summarizes the distances in miles of 120 patients from a regional...

3. The following frequency table summarizes the distances in miles of 120 patients from a regional hospital. Distance Frequency 0-4 40 4-8 30 8-12 20 12-16 20 16-20 10 Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean).

A)In a study of distances traveled by buses before the first major engine failure, a sample...

A)In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles. Calculate the p-value corresponding to the test statistic used to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles and determine if the null hypothesis can be rejected at α = .01. b) A major car manufacturer...

Consider the following data on distances traveled by 100 people to visit the local park. distance...

Consider the following data on distances traveled by 100 people to visit the local park. distance frequency 1-8 30 9-16 25 17-24 25 25-32 10 33-40 10 Expand and construct the table adding columns for relative frequency and cumulative relative frequency. Then plot Histogram, Frequency Polygon and Ogive Curve.

Q2. Distance (000, miles) traveled by a truck in a year is distributed normally with μ...

Q2. Distance (000, miles) traveled by a truck in a year is distributed normally with μ = 50.0 and σ = 12.0. Find a. the proportion of trucks are expected to travel from 34.0 to 59 (000, miles)? (0.6816) b. the probability that a randomly selected truck travels from 34.0 to 38.0 (000, miles)? (0.0669) c. the %age of trucks that are expected to travel either below 30.0 or above 59.0 (000 miles) ? (27.41) d. how many of...

In a random sample of eleven people, the mean driving distance to work was 23.3 miles...

In a random sample of eleven people, the mean driving distance to work was 23.3 miles and the standard deviation was 5.4 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean μ. Interpret the results. Identify the margin of error. (round to one decimal place)

In a random sample of five people, the mean driving distance to work was 25.4 miles...

In a random sample of five people, the mean driving distance to work was 25.4 miles and the standard deviation was 5.2 miles. Assume the random variable is normally distributed and use a t-distribution to find the margin of error and construct confidence intervals for the population mean at the following confidence levels: a. 85% b. 90% c. 99%

Following are the number of miles traveled for 30 randomly selected business flights within the United...

Following are the number of miles traveled for 30 randomly selected business flights within the United States during 1999. 1095, 925, 1656, 1605, 1503, 1928, 2030, 1418, 500, 1248, 2047, 1027, 1962, 1027, 1197, 1928, 874, 1367, 1129, 1401, 874, 602, 1503, 1469, 636, 1503, 925, 1384, 874, 704 a) Use the data to obtain a point estimate for the population mean number of miles traveled per business flight, μ, in 1999. Note: The sum of the data is 38341....