Question

In: Statistics and Probability

Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 2.842 ​g/mi and...

Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 2.842 ​g/mi and standard deviation 0.7 g/mi. A company has 80 of these cars in its fleet. Let y (overbar) represent the mean CO level for the​ company's fleet.

​a) What's the approximate model for the distribution of y (overbar)​? Explain.

​b) Estimate the probability that y (overbar) is between 2.9 and 3 g/mi.

​c) There is only a 5% chance that the​ fleet's mean CO level is greater than what​ value?

Solutions

Expert Solution

a)

~ N ( , / sqrt(n) ) = N ( 2.842 , 0.7/sqrt(80 ) )

b)

P ( 2.9 < < 3 ) = ?
Standardizing the value
Z = ( y - µ ) / ( σ / √(n))
Z = ( 2.9 - 2.842 ) / ( 0.7 / √(80))
Z = 0.74
Z = ( 3 - 2.842 ) / ( 0.7 / √(80))
Z = 2.02
P ( 0.74 < Z < 2.02 )
P ( 2.9 < < 3 ) = P ( Z < 2.02 ) - P ( Z < 0.74 )
P ( 2.9 < < 3 ) = 0.9783 - 0.7704
P ( 2.9 < < 3 ) = 0.2079

c)

P ( > y ) = 1 - P ( < y ) = 1 - 0.05 = 0.95
To find the value of y
Looking for the probability 0.95 in standard normal table to calculate Z score = 1.6449
Z = ( y - µ ) / ( σ / √(n) )
1.6449 = ( y - 2.842 ) / (0.7/√(80))
= 2.971


Related Solutions

Carbon monoxide? (CO) emissions for a certain kind of car vary with mean 3.977 ?g/mi and...
Carbon monoxide? (CO) emissions for a certain kind of car vary with mean 3.977 ?g/mi and standard deviation 0.7 ?g/mi. A company has 60 of these cars in its fleet. Let y overbar represent the mean CO level for the? company's fleet. ? a) What's the approximate model for the distribution of y overbar?? Explain. ?b) Estimate the probability that y overbar is between 4.1 and 4.3 ?g/mi. ? c) There is only a 10?% chance that the? fleet's mean...
Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 2.3 g/mi and...
Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 2.3 g/mi and standard deviation 0.7 g/mi. A company has 80 of these cars in its fleet. Let y(overbar) represent the mean CO level for the​ company's fleet. ​a) Estimate the probability that y(overbar) is between 2.4 and 2.6 g/mi. ​b) There is only a 55​% chance that the​ fleet's mean CO level is greater than what​ value? Show your work on TI-84
Carbon monoxide (CO) emissions for a certain kind of car vary with mean 3 g/mi and...
Carbon monoxide (CO) emissions for a certain kind of car vary with mean 3 g/mi and standard deviation 0.5 g/mi. A company has 81 of these cars in its fleet. a) What’s the approximate model for the distribution of the mean CO level for the company's fleet. Explain. b) Estimate the probability that the mean emission is between 3.0 and 3.1 g/mi. c) There is only a 5% chance that the fleet’s mean CO level is greater than what value?
Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 3.704 ​g/mi and...
Carbon monoxide​ (CO) emissions for a certain kind of car vary with mean 3.704 ​g/mi and standard deviation 0.7 ​g/mi. A company has 70 of these cars in its fleet. Let y overbary represent the mean CO level for the​ company's fleet. ​a) What's the approximate model for the distribution of y overbary​? Explain. ​b) Estimate the probability that y overbary is between 3.8 and 3.9​g/mi. ​c) There is only a 11​% chance that the​ fleet's mean CO level is...
Carbon monoxide emissions for a particular car vary with an average of 2.5 g/mi and a...
Carbon monoxide emissions for a particular car vary with an average of 2.5 g/mi and a standard deviation of 0.3 g/mi. A company has 60 of these cars in its fleet. If X= the CO level for the company's fleet, what is the probability that the average of the 60 cars falls between 2.55 and 2.6 g/mi? Round your answer to four decimal places .
Carbon monoxide (CO) emissions from internal combustion engines increase in colder climates. Thus, the environmental damage...
Carbon monoxide (CO) emissions from internal combustion engines increase in colder climates. Thus, the environmental damage from CO emissions is worse in the winter months than in the summer months. Nonetheless, air quality control authorities use a standard for CO that is uniform throughout the year with no allowance for seasonal effects. The cost and benefit information are as follows: MSB of CO abatement in winter = 350 - 0.5A MSB of CO abatement in summer = 140 - 0.2A...
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain...
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not? TAR NICOTINE CO 6 0.4 5 15 1.0 18 16 1.3 16 13 0.7 18 13 0.8 18 13 0.9 14 16 1.0 17 16...
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain...
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not? Tar   Nicotine   CO 5   0.5   5 17   1.0   19 16   1.1   18 13   0.7   19 13   0.8   18 15   1.1   13 15   1.0   17 16  ...
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain...
The accompanying table provides data for​ tar, nicotine, and carbon monoxide​ (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it​ best? Is the best regression equation a good regression equation for predicting the nicotine​ content? Why or why​ not? Tar   Nicotine   CO 5   0.5   3 15   1.0   19 17   1.1   16 14   0.7   19 14   0.8   19 14   1.0   13 15   1.0   16 14  ...
5. Consider the combustion of carbon monoxide (CO) in oxygen gas: 2CO(g) + O2(g) → 2CO2(g)...
5. Consider the combustion of carbon monoxide (CO) in oxygen gas: 2CO(g) + O2(g) → 2CO2(g) A. Calculate the number of moles of CO2 produced if 2.86 moles of CO is reacted with excess oxygen._______ moles CO2. B. Determine the moles of oxygen required to react with the CO._______ moles O2 6. Consider the following balanced chemical equation: C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l) a. How many moles of CO2 form when 1.73 moles of C2H5OH react? ______ moles...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT