00:01
Hello everyone in this question it is said that an elevator that has maximum capacity is 445 lb for 15 passengers if 15 males adult males can have a mean weight up to 15 adult male passengers is equals to 2 .44 divided by 5, divide by 15 is equals to 163 pounds.
00:56
If elevator is loaded with 15 adult male passengers, what is the probability that it is overloaded? probability that elevator is overloaded.
01:11
That elevator is overloaded which means the mean weight is greater than 163 pounds.
01:25
So assume that mean weight of meals are normally distributed with 166, 166 lb, and standard aviation is 33 lb.
01:42
We also have to say that does this elevator appears to be safe? does this elevator appears to be safe? appears to be safe.
01:59
So first of all, we have to find the probability that elevator is overloaded, which means we have to find the probability that mean is greater than 163, which becomes equal to probability that x bar subtracted with mu divided by sigma with number of passengers greater than 163, mean is 166 divided by 33, which is also divided by square root of 15, because number of passengers are 15 passengers.
02:37
So when we solve this, we get probability.
02:40
This term is denoted with z, z score, and when we solve this, we get a square root of 15, multiplied with negative of 3 divided by 33.
02:53
When we done all the calculation, we get p, z is greater than negative of 0 decimal 3.
03:01
To find the probability that z is greater than this, we can write it as a 1 minus probability of z is less than negative of 0 .3 .5.
03:15
To find this value, use z value table...