Answer:
Step-by-step 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
[tex]P(x>112)=P(z>\frac{112-110}{5})\\\\=P(z>0.4)=0.3446[/tex]
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%
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. Â
We want to find out the probability that the electric device works more than 112 hours Â
[tex]P(X > 112) = 1 - P(X < 112)\\\\P(X > 112) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 112) = 1 - P(Z < \frac{112 - 110}{5} )\\\\P(X > 112) = 1 - P(Z < \frac{2}{5} )\\\\P(X > 112) = 1 - P(Z < 0.4)\\\\[/tex]
The z-score from the z-table corresponding to 0.4 is 0.6554
[tex]P(X > 112) = 1 - 0.6554\\\\P(X > 112) = 0.3446 \\\\P(X > 112) = 34.46 \%[/tex]
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.
