Hi,
I need help with the setup of this problem.
The capacity for the elevator is 2500 kgs. Baseball players have weights that are normally distributed with a mean of 120 kgs and a standard dev. of 80 kgs. 25 baseball players get on the elevator. What is the likelihood that the cable will snap?
I set it up as Z= (X-µ) / σ but what is X ?
You may be using Z-values that start at zero or a table of positive and negative z-values,
as clearly in this case z is negative.
In this example you are calculating the probability that Z is greater that your z-score.
Hence, if you only have positive values of z, you need to find the probability
that Z is less than the modulus of your z-score.
Since the average weight of the 25 players exceeds the breaking strain of the cable,
there is a more than 50 percent chance the cable will snap.
You could also calculate
and look up the probability that
which is about 0.6
Z tables give you the probability of z being less than or equal to some z-score. the normal distribution is symmetrical about the mean,
so there is flexibility in making calculations.
The random variable is where ~ Normal .
You're expected to know that the sum of normal random variables is also a normal random variable: Sum of normally distributed random variables - Wikipedia, the free encyclopedia.
You should therefore know that in this case, W ~ Normal .
Use the distribution of W to calculate Pr(W > 2500).
Haven't you been taught how to calculate probabilities from a normal distribution? What do your classnotes and textbook say about getting the z-value, using tables etc. (Is this the very first question about calculating probability from a normal distribution that you have ever tried?)
I took one statistics class 3 years ago. The class is econometrics and I have 8 pages of class notes that are not helpful and contain little in the form of valuable examples which is why I'm on here. I've spent hours on this homework trying to understand and at this point I'm just trying to work my way backwards since the professor has not responded to my emails either. I plan on going to a tutor on Monday but I want to see what it is that I need help with! Thanks for responding anyway.
You also need to substitute W = 2500. Therefore Z = -1.25.
Step 2: Calculate Pr(Z > -1.25).
Note that Pr(Z > -1.25) = Pr(Z < 1.25) using the symmetry of the normal distribution. Pr(Z < 1.25) is something you can look up in your standard normal distribution tables ....