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horrorfan [7]
3 years ago
7

A researcher wants to estimate the mean commute time of residents in Westchester County. The researcher samples 40 commuters and

find the mean commute time to be 25 minutes. Assume the population standard deviation for commute time is 12.5 minutes. Construct a 90% confidence interval for the mean commute time of residents in Westchester County. What is the Lower Bound of the confidence interval
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
4 0

Answer:

21.759

Step-by-step explanation:

Given that :

Mean (m) = 25

Standard deviation (s) = 12.5

Sample size (n) = 40

α = 90%

The confidence interval is obtained using the relation:

Mean ± Zcritical * s/sqrt(n)

Zcritical at 90% confidence interval = 1.64

25 ± 1.64 * (12.5/sqrt(40))

Lower boundary : 25 - 1.64(1.9764235) = 21.75866546

Upper boundary : 25 + 1.64(1.9764235) = 28.24133454

(21.759, 28.241)

Hence, lower bound of confidence interval is : 21.759

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Answer:

$10,000

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3 years ago
If the fuel tank in Jim's car holds 14 gallons of fuel, define a formula to determine the number of gallons of fuel in Jim's fue
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Considering that the car does 50 miles per gallon, the linear function for the number of gallons of fuel in Jim's fuel tank, n, in terms of the number of miles x that Jim has driven since filling his tank is given by:

y = -0.02x + 14

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

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In this problem:

  • Jim's car holds 14 gallons of fuel, hence b = 14.
  • Considering it does 50 miles per gallon, and the amount in the tank will decrease, the slope is m = -\frac{1}{50} = -0.02.

Hence, the function is:

y = -0.02x + 14

You can learn more about linear functions at brainly.com/question/25898120

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