Answer: P(9950 ≤ x ≤ 10250) = 0.54
Step-by-step explanation:
We would assume a normal distribution for the breaking strength of a rivet. We would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ/√n
Where
n = number of samples
x = Breaking strengths of rivet.
µ = mean breaking strength
σ = standard deviation
From the information given,
µ = 10,050 psi
σ = 499 psi
n = 40
The probability that the sample mean breaking strength for a random sample of 40 rivets is between 9,950 and 10,250 is expressed as
P(9950 ≤ x ≤ 10250)
For x = 9950,
z = (9950 - 10050)/499/√40 = - 0.13
Looking at the normal distribution table, the probability corresponding to the z score is 0.45
For x = 10250,
z = (10250 - 10050)/499/√40 = 2.54
Looking at the normal distribution table, the probability corresponding to the z score is 0.99
Therefore,
P(9950 ≤ x ≤ 10250) = 0.99 - 0.45 = 0.54
