Question

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

Answer 1

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) = ?

Answer:

P(X > 112) = 34.46%

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

`P(X > 112) = 1 - P(X < 112)\\\\P(X > 112) = 1 - P(Z < (x - \mu)/(\sigma) )\\\\P(X > 112) = 1 - P(Z < (112 - 110)/(5) )\\\\P(X > 112) = 1 - P(Z < (2)/(5) )\\\\P(X > 112) = 1 - P(Z < 0.4)\\\\`

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

`P(X > 112) = 1 - 0.6554\\\\P(X > 112) = 0.3446 \\\\P(X > 112) = 34.46 \%`

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.

Answer 2

Therefore, So the correct answer is 0.3446

Explanation:

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

Here it is given that distribution is normal with

mean = 110 and standard deviation = 5

Now we need to find

P (x > 112)

As distribution is normal we can convert x to z

`P(x>112)=P(z>(112-110)/(5))\\\\=P(z>0.4)=0.3446`

Therefore, So the correct answer is 0.3446