Suppose in December 2019, the average and standard deviation of gas price at gas stations were...

Suppose in December 2019, the average and standard deviation of gas price at gas stations were 136.5 and 6 ¢/liter respectively. A random sample of n = 36 gas stations is selected from the population and the price per liter of gas is determined for each.

a) Describe the distribution of the average gas price determined for this sample gas stations. What are the values of mean and standard deviation for this distribution?

b) What is the probability that the mean gas price of the sample is between 135 ¢/liter and 138 ¢/liter?

c) Suppose we wish to estimate the average gas price within 0.9 ¢/liter of its true value with a 95% confidence interval. What sample size should be specified for the experiment? (σ ≈ 6)

Solutions

Expert Solution

According to the Central Limit Theorem, the distribution of the average gas price is Normal distribution.

mean = 136.5

standard deviation = 6 / = 1

Probability that the mean gas price of the sample is between 135 ¢/liter and 138 ¢/liter

= P(135 < < 138)

= P( < 138) - P( < 135)

= P[Z < (138 - 136.5)/1] - P[Z < (135 - 136.5)/1]

= P[Z < 1.5] - P[Z < -1.5]

= 0.9332 - 0.0668

= 0.8664

Margin of error, E = 0.9 ¢/liter

Standard deviation, = 6

Z score for 95% confidence interval is 1.96

Sample size , n = = 170.7378

171 (Rounded to nearest integer)

orchestra answered 1 year ago

Next > < Previous

Related Solutions

You are interested in the in analyzing the price of gas at all the service stations...

You are interested in the in analyzing the price of gas at all the service stations you pass on your way to work in the morning. You gather the following prices: $4.05 $3,95, $3.98, $3.85, $3.71, $3.69, $3.95, $3.29, $3.84, $3.97, and $4.00. Based on these numbers, provide the mean, median, mode and standard deviation.

1. The average price for a new car is $18,000 and the standard deviation is $1,500....

1. The average price for a new car is $18,000 and the standard deviation is $1,500. Calculate the z scores for the following individual scores. SHOW YOUR WORK.If X = 19,000, z = _ 2. Using z-scores. SHOW YOUR WORK The percent of area beyond z = 1.44 is 3. Using z-scores. SHOW YOUR WORK ).The percent of area between the z = 1.40 and z = 1.49 is ________. 4. Using z-scores. SHOW YOUR WORK The percent of TOTAL...

The average price of a college math textbook is $171 and the standard deviation is $20....

The average price of a college math textbook is $171 and the standard deviation is $20. Suppose that 17 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. A. What is the distribution of ¯x? ¯x ~ N( , ) B. For the group of 17, find the probability that the average price is between $172 and $176. C. Find the third quartile for the average textbook price for this sample size. $ (round to the...

A town’s December high temperatures average 46 oF with a standard deviation of 9 oF, while...

A town’s December high temperatures average 46 oF with a standard deviation of 9 oF, while in June the mean height temperature is 75 oF with a standard deviation of 8 oF. In which month is it more unusual to have a high temperature of 64 oF? a. June because the z-score is farther away from zero than for December b. June because the z-score is closer to zero than for December. c. December because the z-score is closer to...

Suppose the average lifespan of a lab rat is 3.4 years with a standard deviation of...

Suppose the average lifespan of a lab rat is 3.4 years with a standard deviation of 0.8 years. If we obtain a simple random sample of 64 lab rats, what is the probability that the sample average lifespan is at least 3.65 years? a) 0.0062 b) 0.9938 c) 0.4052 d) 0.0485 e) 0.9515

Suppose the average return on Asset A is 7.0 percent and the standard deviation is 8.2...

Suppose the average return on Asset A is 7.0 percent and the standard deviation is 8.2 percent and the average return and standard deviation on Asset B are 4.1 percent and 3.5 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 11 percent? Less than 0 percent? (Round your...

Suppose that the average annual revenue of a small business is $150,000 with a standard deviation...

Suppose that the average annual revenue of a small business is $150,000 with a standard deviation of $40,000. Assume that the revenue distribution is normal. 1. What is the probability that one business selected at random makes less than $120,000? 2. What is the probability that the average annual revenue of a random sample of 4 businesses is less than $120,000? 3. Why are your answers to the previous two questions different?

Suppose the average return on an asset is 12.3 percent and the standard deviation is 20.8...

Suppose the average return on an asset is 12.3 percent and the standard deviation is 20.8 percent. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to determine the probability that in any given year you will lose money by investing in this asset. Probability?

Suppose the average return on Asset A is 6.8 percent and the standard deviation is 8.8...

Suppose the average return on Asset A is 6.8 percent and the standard deviation is 8.8 percent, and the average return and standard deviation on Asset B are 4 percent and 3.4 percent, respectively. Further, assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. a. What is the probability that in any given year, the return on Asset A will be greater than 10 percent? Less than 0 percent? (Do not...

Suppose the guests at the hotel have an average weight of 180 with a standard deviation...

Suppose the guests at the hotel have an average weight of 180 with a standard deviation of 50 pounds. An elevator is designed to carry only 10 people with a maximum capacity of 2400 pounds. 5. What is the mean of the sample mean? 6. What is the standard deviation for the sample mean of the 10 people? (Use 2 decimals) 7. If 10 guest ride the elevator at one time, what is the probability that the elevator is overweight?...

Subjects