An electric device consists of Two parts, A and B. The electric device works if both parts work. Suppose parts A and B have a lifetime that is normally distributed with mean 110 hours and standard deviation 5 hours. Suppose further that parts A and B work independent of each other. What is the probability that the electric device works more than 112 hours

Given Information:

Mean lifetime of electric device = μ = 110 hours

Standard deviation of lifetime of electric device = σ = 5 hours

Required Information:

P(X > 112) = ?

P(X > 112) = 34.46%

Step-by-step explanation:

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

We want to find out the probability that the electric device works more than 112 hours  

The z-score from the z-table corresponding to 0.4 is 0.6554

Therefore, there is 34.46% probability that the electric device works more than 112 hours.

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.6, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.6 then go for 0.00 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

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answer:

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step-by-step explanation: