A woman exerts a horizontal force of 10 pounds on a box as she pushes it up a ramp that is 8 feet long and inclined at an angle
1 answer:
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Answer:
<em>The probability of spending between 4 and 7 days in recovery</em>
<em>P(4≤x≤7) = 0.5445</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given mean of the Population μ = 5.3 days
Given standard deviation of the population 'σ' = 2 days
Let 'X' be the random variable in normal distribution
Let x₁ = 4
Let x₂ = 7
<u><em>Step(ii):-</em></u>
<u><em>The probability of spending between 4 and 7 days in recovery</em></u>
<em>P(4≤x≤7) = P(-0.65≤Z≤0.85)</em>
<em> = P(Z≤0.85) - P(Z≤-0.65)</em>
<em> = 0.5 + A( 0.85) - ( 0.5 - A(-0.65) </em>
<em> = 0.5 + A( 0.85) - 0.5 +A(0.65) ( ∵A(-0.65) = A(0.65)</em>
<em> = A(0.85) + A(0.65)</em>
<em> = 0.3023 + 0.2422</em>
<em> = 0.5445</em>
<u><em>Final answer:</em></u><em>-</em>
<em>The probability of spending between 4 and 7 days in recovery</em>
<em>P(4≤x≤7) = 0.5445</em>
<em> </em>
Answer:
Population Mean = 2.0
Population Standard deviation = 0.03
Step-by-step explanation:
We are given that the inspector selects simple random samples of 30 finished products and computes the sample mean product weight.
Also, test results over a long period of time show that 5% of the values are over 2.1 pounds and 5% are under 1.9 pounds.
Now, mean of the population is given the average of two extreme boundaries because mean lies exactly in the middle of the distribution.
So, Mean, =
= 2.0
Therefore, mean for the population of products produced with this process is 2.
Since, we are given that 5% of the values are under 1.9 pounds so we will calculate the z score value corresponding to a probability of 5% i.e.
z = -1.6449 {from z % table}
We know that z formula is given by ;
~ N(0,1)
-1.6449 = ⇒
⇒ 0.0608 *
{as sample size is given 30}
⇒ = 0.03 .
Therefore, Standard deviation for the population of products produced with this process is 0.0333.