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The combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range 22 mpg to 25 mpg. (a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution) from Table 8.11. (Round your answer to 4 decimal places.)  Standard deviation        _________      (b) What sample size is needed to estimate the mean with 98 percent confidence and an error of ± 0.25 mpg? (Enter your answer as a whole number (no decimals). Use a z-value taken to 3 decimal places in your calculations.)  Sample size            _________

Question

The combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range 22 mpg to 25 mpg.
 
(a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution) from Table 8.11. (Round your answer to 4 decimal places.)
  
Standard deviation        _________     
 
(b) What sample size is needed to estimate the mean with 98 percent confidence and an error of ± 0.25 mpg? (Enter your answer as a whole number (no decimals). Use a z-value taken to 3 decimal places in your calculations.)
  
Sample size            _________

check_circleAnswer
Step 1

Given Data

Range from 22 mpg to 25 mpg

a = 22 mpg

b = 25 mpg

a) Standard Deviation using method 3 for normal distribution is calculated as

b - a
σ=
6
25 22
= 0.5
σ=
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b - a σ= 6 25 22 = 0.5 σ=

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Step 2

b)

Estimation of sample size...

Error (E) 25% = 0.25
Confidence level = 0.98
Significance level = a = 1 - 0.98 = 0.02
Zo.02
Zo.01 = -2.32635
1
2
(Using Excel -NORM.S.INV (0.01))
Formula to calculate sample size
2
2
2.32635 x 0.5
Zo.01
= 21.647 = 22
1
0.25
E
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Error (E) 25% = 0.25 Confidence level = 0.98 Significance level = a = 1 - 0.98 = 0.02 Zo.02 Zo.01 = -2.32635 1 2 (Using Excel -NORM.S.INV (0.01)) Formula to calculate sample size 2 2 2.32635 x 0.5 Zo.01 = 21.647 = 22 1 0.25 E

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