Question

In: Statistics and Probability

The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year...

The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal​ distribution, as shown in the figure. ​(a) What consumption level represents the 7th ​percentile? ​(b) What consumption level represents the 21st ​percentile? ​(c) What consumption level represents the third ​quartile? mean=2302 SD=584.5

Solutions

Expert Solution

Given that,

mean = = 2302

standard deviation = = 584.5

Using standard normal table,

P(Z < z) = 7%

= P(Z < z) = 0.07  

= P(Z <-1.48 ) = 0.07

z = -1.48 Using standard normal table,

Using z-score formula  

x= z * +

x= -1.48*584.5+2302

x= 1436.94

x=1437

(B)

Using standard normal table,

P(Z < z) = 21%

= P(Z < z) = 0.21  

= P(Z <-0.81) = 0.21

z = -0.81 Using standard normal table,

Using z-score formula  

x= z * +

x= -0.81 *584.5+2302

x= 1828.555

x=1829

(C)

The z dist'n Third quartile is,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.67 ) = 0.75

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 584.5+2302

x = 2693.615

x=2694


Related Solutions

The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year...
The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal​ distribution, as shown in the figure. Mean=2296 Standard deviation=581.8 ​(a) What consumption level represents the 5 th ​percentile? ​ (b) What consumption level represents the 17 th ​percentile? ​(c) What consumption level represents the third ​quartile?
2) The file ‘Energy’ contains the per capita energy consumption (in kilowatt-hours), for each of the...
2) The file ‘Energy’ contains the per capita energy consumption (in kilowatt-hours), for each of the 50 states and the District of Columbia during a recent year. a) Compute the mean, variance, and standard deviation for the population. b) What proportion of these states has per capita energy consumption within + or – 1 standard deviation of the mean, within + or – 2 standard deviations of the mean, and within + or – 3 standard deviations of the mean?...
In​ 2008, the per capita consumption of soft drinks in Country A was reported to be...
In​ 2008, the per capita consumption of soft drinks in Country A was reported to be 18.15 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally​ distributed, with a mean of 18.15 gallons and a standard deviation of 5 gallons. Complete parts​ (a) through​ (d) below . a. What is the probability that someone in Country A consumed more than 10 gallons of soft drinks in​ 2008? The probability is nothing. ​(Round to...
In​ 2008, the per capita consumption of coffee in Country A was reported to be 19.37...
In​ 2008, the per capita consumption of coffee in Country A was reported to be 19.37 pounds. Assume that the per capita consumption of coffee in Country A is approximately normally​ distributed, with a mean of 19.37 pounds and a standard deviation of 4 pounds. Complete parts​ (a) through​ (d) below. a. What is the probability that someone in Country A consumed more than 13 pounds of coffee in​ 2008? b. What is the probability that someone in Country A...
In​ 2008, the per capita consumption of soft drinks in Country A was reported to be...
In​ 2008, the per capita consumption of soft drinks in Country A was reported to be 19.31 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally​ distributed, with a mean of 19.31 gallons and a standard deviation of 4 gallons. Complete parts​ (a) through​ (d) below. a. What is the probability that someone in Country A consumed more than 14 gallons of soft drinks in​ 2008? b. What is the probability that someone...
In​ 2008, the per capita consumption of soft drinks in Country A was reported to be...
In​ 2008, the per capita consumption of soft drinks in Country A was reported to be 19.35 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally​ distributed, with a mean of 19.35 gallons and a standard deviation of 4 gallons. Complete parts​ (a) through​ (d) below. a. What is the probability that someone in Country A consumed more than 14 gallons of soft drinks in​ 2008? The probability is nothing. ​(Round to four...
According to a recent study annual per capita consumption of milk in the United States is...
According to a recent study annual per capita consumption of milk in the United States is 22.6 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered into the Microsoft Excel Online file below. Use the data to set up your spreadsheet and test your hypothesis. 25.8 23.84 25.25 21.2...
According to a recent study annual per capita consumption of milk in the United States is...
According to a recent study annual per capita consumption of milk in the United States is 21.5 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered into the Microsoft Excel Online file below. Use the data to set up your spreadsheet and test your hypothesis. Given Data: Gallons of...
According to a recent study annual per capita consumption of milk in the United States is...
According to a recent study annual per capita consumption of milk in the United States is 21.5 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered into the Microsoft Excel Online file below. Use the data to set up your spreadsheet and test your hypothesis. 24.8 23.84 25.25 21.3...
According to a recent study annual per capita consumption of milk in the United States is...
According to a recent study annual per capita consumption of milk in the United States is 21.5 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption below. Gallons of Milk 27.1 23.84 25.25 21 17.52 19.61 19.83 26.18 34.97 29.9 28.59 20.57 26.94 27.24 Develop a hypothesis test that can be...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT