Mathematics: How many -foot pieces of ribbon can be cut from a piece of ribbon that is 36 feet long? A 18 pieces B 19 pieces C 20 pieces D 21 pieces

How many -foot pieces of ribbon can be cut from

skinman

06.10.2021

a) The probability that a single randomly selected value is greater than 27.6

P( X≥27.6) = 0.8051

b) The probability that a sample of size randomly selected value is greater mean greater than 27.6

P( X≥27.6) = 0.9998

Step-by-step explanation:

Step(i):-

Given that the mean of the Population = 30 weeks

The Standard deviation of the Population = 2.8 weeks

Let 'X' be a Normal distribution

$Z = \frac{x-mean}{S.D} = \frac{27.6-30}{2.8} = -0.857$

The probability that a single randomly selected value is greater than 27.6

P( X≥27.6) = P(Z≥-0.857)

= 0.5 + A(-0.857)

= 0.5 + A(0.857)

= 0.5 + 0.3051

= 0.8051

Step(ii):-

Let 'X' be a Normal distribution

$Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } } = \frac{27.6-30}{\frac{2.8}{\sqrt{80} } } = -7.6677$

The probability that a sample of size randomly selected value is greater mean greater than 27.6

P( X≥27.6) = P(Z≥-7667)

= 0.5 + A(-7.667)

=0.5 +0.4998

= 0.9998

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