Respuesta :
Answer:
Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.
Step-by-step explanation:
We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.
A random sample of 39 steel bolts is selected.
Let [tex]\bar X[/tex] = sample mean diameter
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean diameter = 141 millimetres
[tex]\sigma[/tex] = standard deviation = 7 millimetres
n = sample of steel bolts = 39
Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P([tex]\bar X[/tex] > 141.4 millimetres)
P([tex]\bar X[/tex] > 141.4) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }[/tex] > [tex]\frac{141.4-141}{\frac{7}{\sqrt{39} } } }[/tex] ) = P(Z > 0.36) = 1 - P(Z [tex]\leq[/tex] 0.36)
= 1 - 0.6406 = 0.3594
The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.
