Problema Solution
The American college of Cordiologists claims that the mean number of grams of fat in the popular M.I. Burger sold at Burgers To Die For is 24 grams with σ =5grams. IF a sample of 50 M.I. Burgers is taken, what is the probability that the sample mean is 25 grams more.
Answer provided by our tutors
Let μ = 25 g be the mean and σ = 5 g the standard deviation and σ N = σ/sqrt(N) the standard deviation of the sample where N = 50
Let X denote the grams of fat of a burger chosen at random from the 50 burgers sample.
The problem is to find P(X > 25)
since z = (X - 25)/σ N we have
P( z > (25 - μ)/(σ/sqrt(50) ) [Substitute μ = 24 and σ = 5]
P( z > (25-24)/(5/sqrt(50) )
P( z > 1.4142)
P(z > 1.4142) = P(z > 0) - P( 0 < z <= 1.4142)
P(z > 1.4142) = 0.5000 - 0.4207 = 0.0793 or 7.93%
[Refer to the table giving the area under the standard normal curve from 0 to z. https&#x3a;&#x2f;&#x2f;www.mathsisfun.com/data/standard-normal-distribution-table.html]
Therefore, the probability that the sample mean is 25 grams more is 7.93%.