# Confidence Interval and Normal Probability

Number 1

The union for a particular industry has determined that the standard deviation of the daily wages Find a 90% confidence interval for the true mean daily wage of all union workers in the industry. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place Standard deviation is 18

Number is 100 of its workers is $ 18. A random sample of 100 workers in this industry has a mean daily wage of $119.

2. Adults who are being tested for dementia are asked to perform mental tasks such as listing as many animals as

they can in one minute. Here are the numbers of animals listed in one minute by normal (non-demented) adults:

19, 25, 12, 16, 12, 12, 10, 18.

(a) What is the median of this data set? If your answer is not an integer, round your answer to at least one decimal place.

(b) What is the mean of this data set? If your answer is not an integer, round your answer to at least one decimal place.

(c) How many modes does the data set have, and what are their values?

Indicate the number of modes by selecting the appropriate line, and then indicate the value(s) of the mode(s), if applicable.

1. zero modes:

2. one mode: ____

3. two modes: _____ _____

3. For each of the variables described below, indicate whether it is a quantitative or a categorical (qualitative) variable.

Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio.

Make sure your responses are the most specific possible.

a)Temperature (Degrees Celsius)

b) Price (in dollars) of a shirt on the clearance

(c) Medal won in a recent race (gold, silver,

4. Which of the following variables are best thought of as continuous, which discrete? Indicate your choice for each by

circling the appropriate answer.

(a) The body temperature measurement of a participant in a lie-detector test.

Discrete Continuous

(b) The length of the arm of a heavyweight boxer.

Discrete Continuous

(c) The time for a participant to identify the color of the letters when the word red is shown in green letters on a computer screen.

Discrete Continuous

(d) The highest grade level (9 ,10 , or 11 ) completed by a high-school dropout.

Discrete Continuous

5. Let be a standard normal random variable. Calculate the following probabilities using the calculator provided.

Round your responses to at least three decimal places.

P(Z<-1.19)=

P(Z> 1.17)=

P(-0.97<Z<2.03)=

7. Let Z be a standard normal random variable. Use the calculator provided to determine the value of such that

P(-1.17<Z<c)=0.8632

.

Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal

places.

8 Suppose that scores on a particular test are normally distributed with a mean of 110 and a standard deviation of 16. What is the minimum score needed to be in the top 2% of the scores on the test?

Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

9. Use the calculator provided to solve the following problems.

Consider a t distribution with 15 degrees of freedom. Compute p(-1.23<t<1.23) . Round your answer to at least three decimal places.

Consider a t distribution with 6 degrees of freedom. Find the value of such that P(t>c)=0.01 . Round your answer to at least three decimal places.

10. Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 40 farm-raised trout is selected. The mean fat content for the sample is 31.1 grams per pound.

Find the probability of observing a sample mean of 31.1 grams of fat per pound or less in a random sample of 40 farm-raised trout.

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal