Exam 6: The Normal Distribution

One normal curve has a mean of 24 and a standard deviation of 3. A second normal curve has a mean of 3 and a standard deviation of 24. The curve that is more dispersed, Or spread out, is

$\text { Find the area under the standard normal distribution curve to the left of } z = 1.69 \text {. }$

The standard deviation of sample means will be larger than the standard deviation of the population.

At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that the employee has worked At the store for over 10 years?

Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 78 , p = 0.59 : P ( X > 42 )$

The mean number of pets per household is 2.96 with standard deviation 1.4. A sample of 52 households is drawn. Find the 74th percentile of the sample mean.

The correction factor is important if a relatively large number of samples are taken without replacement from a small population.

In applied statistics, it is the area under the normal distribution curve which is most important, not the value of single points on the curve.

The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that the distribution of contributions is normal with a standard deviation Of $103. Find the limits for the middle 50% of contributions.

A certain car model has a mean gas mileage of 28 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 37 of these cars. What is the probability That the average mileage of the fleet is between 27.2 and 28.8 mpg?

$\text { Find the area under the standard normal distribution curve between } z = 0 \text { and } z = 2.16 \text {. }$

The average diameter of sand dollars on a certain island is 3.00 centimeters with a standard deviation of 1.00 centimeters. If 9 sand dollars are chosen at random for a Collection, find the probability that the average diameter of those sand dollars is more Than 2.60 centimeters. Assume that the variable is normally distributed.

The mean annual income for people in a certain city (in thousands of dollars) is 43, with a standard deviation of 29. A pollster draws a sample of 41 people to interview. What is The probability that the sample mean income is less than 42 (thousands of dollars)?

The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of Institution, the salary is $90,330. If the standard deviation for the salaries of both genders Is approximately $5200 and the salaries are normally distributed, find the 80th percentile Salary for the male professors and for female professors, respectively.

What is the area under the standard normal distribution curve between $z = 1.50$ and $z = 2.50 ?$

The average number of mosquitos in a stagnant pond is 80 per square meter with a standard deviation of 12. If 36 square meters are chosen at random for a mosquito count, Find the probability that the average of those counts is more than 81.8 mosquitos per Square meter. Assume that the variable is normally distributed.

$\text { The figure below is an example of a negatively skewed distribution. }$

A ferry will safely accommodate 91 tons of passenger cars. Assume that the mean weight of a passenger car is 2.1 tons with standard deviation 0.7 tons. If a random sample of 40 Cars are loaded onto the ferry, what is the probability that the maximum safe weight will Be exceeded?

$X$ is a normally distributed random variable with a mean of $4.0$ . Find the standard deviation of the distribution if $59.10 \%$ of the data lies to the right of $3.54$ . (Note: the diagram is not necessarily to scale.)