Question

Questions A and B must be answered using a pencil and paper.

A.) A manufacturing line is powered by an electrical plant. The burning rate of the plant is approximately normally distributed with a variance of 4 cm/sec² and a mean of 50 cm/sec. What is the probability that the mean burning rate will be between 46 cm/sec and 50cm/sec?

B.) The burning rate of the plant was sampled 25 times. What is the probability that the sample mean will be above 51.3 cm/sec?

Answer 1

Solution :

Given that,

mean = = 50

variance = ² = 4

standard deviation = = 2

a ) P (46 < x < 331 )

P ( 46 - 50 / 2) < ( x -  / ) < ( 50 - 50 / 2)

P ( - 4 / 2 < z < 0 / 2 )

P (-2 < z < 0)

P ( z < 0 ) - P ( z < -2)

Using z table

= 0.5000 - 0.0228

= 0.4772

Probability = 0.4772

b ) n =25

=50

₌ / n = 2 25 = 0.4

P ( > 51.3 )

= 1 - P ( < 51.3 )

= 1 - P ( - /  ) < ( 51.3 - 50 / 0.4 )

= 1 - P ( z < 1.3 / 0.4 )

= 1 - P ( z < 3.25)

Using z table

= 1 - 0.9994

= 0.0006

Probability = 0.0006