Question

8. A paint line can completely paint a produce with a mean time of 40 minutes with a standard deviation of 12 minutes. Nine items are selected at random to be painted.

Answer 1

mean = 40 and sd = 12

a)

P(35 <X < 45)

= P((35 - 40)/(12/sqrt(9)) < z < (45 - 40)/(12/sqrt(9)))

= P(-1.25 < z < 1.25)

= 0.7887

b)

P(X > 50)

= P( z > (50 - 40)/(12/sqrt(9)))

= P(z > 0.9938)

= 0.0062

c)

Given CI Level = 95%

Margin of Error(ME) = 4

std. dev. = 12

z-value of 95% CI = 1.9600

n = (z*sigma/ME)^2

n = (1.96*12/4)^2

= 35