Question

Suppose that a manufactured part has a length which is normally distributed with mean 5cm and standard deviation 2mm. What is the probability that a randomly inspected part will have a length between 4.75cm and 5.05cm?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 5

standard deviation = $\sigma$ = 2

P(4.75< x < 5.05) = P((4.75 - 5)/ 2) < (x - $\mu$ ) /$\sigma$  < (5.05 - 5) / 2) )

= P(-0.13 < z < 0.03)

= P(z < 0.03) - P(z < -0.13)

= 0.5120 -  0.4483 Using standard normal table,  

Probability = 0.0637