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The distribution of the amount of water used per wash cycle, in gallons, by a particular brand of dishwasher during a wash cycle is approximately normal with mean 4 gallons and standard deviation 0. 2 gallon. Which of the following is closest to the probability that more than 3. 75 gallons are used for any wash cycle?.

Answer :

Onyebuchinnajigo

The probability that more than 3.75 gallons will be used for any washing cycle is 0.89.

The given parameters:

  • Mean of the distribution, M = 4 gallons
  • Standard deviation, d = 0.2 gallon

The probability of using more than 3.75 gallons is calculated as follows;

P(more than 3.75 gallons) = 1 - P(3.75 gallons)

For a normal distribution curve, the following probability exists;

  • 1 standard deviation below the mean = M - d = 14%
  • 2 standard deviation below the mean = M - 2d = 2%

The number of gallons used for washing at 1 standard deviation below the mean;

n = M - d

n = 4 - 0.2

n = 3.8 gallons

The number of gallons used for washing at 2 standard deviation below the mean;

n = M - 2d

n = 4 - 2(0.2)

n = 3.6 gallons

The probability of exactly 3.75 gallons is determined by interpolation:

3.6 ------------- 2%

3.75 -------------- x

3.8 --------------- 14%

[tex]\frac{3.75 - 3.6}{3.8 - 3.6} = \frac{x - 2}{14-2} \\\\\frac{0.15}{0.2} = \frac{x-2}{12} \\\\0.2(x-2) = 12(0.15)\\\\0.2x - 0.4 = 1.8\\\\0.2x = 1.8 + 0.4\\\\0.2x = 2.2\\\\x = \frac{2.2}{0.2} \\\\x = 11 \ \%[/tex]

The probability of using exactly 3.75 gallons for washing = 11%

The probability that more than 3.75 gallons will be used for any washing cycle is calculated as follows;

P = 100% - 11%

P = 1 - 0.11

P = 0.89

Learn more about normal distribution curve here: https://brainly.com/question/14644201

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