Question

An electronic product takes an average of 10 hours to move through an assembly line. If the standard deviation is 0.3 hours, what is the probablity that an 3 hours,what is the probability that an tem will take between 9.5 and 9.7 hours move to move through the assembly line? Assume that the distribution is normal. (Round your answer to 3 decimal places, and report a probability value between 0 and 1.) Answer

Answer 1

Solution :

Given that ,

mean = $\mu$ = 10

standard deviation = $\sigma$ = 0.3

P(9.5 < x < 9.7) = P((9.5 - 10 / 0.3) < (x - $\mu$ ) / $\sigma$ < (9.7 - 10) / 0.3) )

P(9.5 < x < 9.7) = P(-1.67 < z < -0.1)

P(9.5 < x < 9.7) = P(z < -0.1) - P(z < -1.67)

P(9.5 < x < 9.7) = 0.1587 - 0.0475 = 0.1112

Probability = 0.111