Question

Doc Brown is concerned that his scientific instrument, the 'flux capacitor', is not receiving enough energy to function properly. To be certain, he measures the energy flow to the instrument in random experiments, measuring the power in gigawatts(Gw). Suppose that the power from all experiments is normally distributed, with a mean of 0.87GW and a standard deviation of 0.75GW. What is the probability that the total from five experiment is less than 5 GW?

Answer 1

Given:

Doc Brown is concerned that his scientific instrument, the 'flux capacitor', is not receiving enough energy to function properly.

Mean, = 0.87

Standard deviation, = 0.75

Let X : the power from all experiments .

X follows the Normal distribution.

X ~ Normal( = 0.87, ^2 = 0.75^2)

The probability that the total from five experiment is less than 5 GW :

P(X < 5 ) = P(X - / < 5 - 0.87 / 0.75)

= P(Z < 5.51)

= 0.0000......(from z table)

Therefore the probability that the total from five experiment is less than 5 GW is 0.0000