I have this question which is stumping me and my lecture is little help.
For part we have to find the standard error and I have that, well I think I do, and part b and c depend on us getting part a right. Can someone please help me out.
The sign on the lift in a building states 'Maximum capacity 1120 kg or 16 persons'. A safety manager
wonders if the sign needs to be changed given that the weights of people who use the lift are normally
distributed with a mean of 68 kg and a standard deviation of 8 kg. The safety manager wants you to help
him with the following questions
(a). What is the standard error of the mean weight for a sample of 16 people?
So i have used the standard error formula and got 2 as the answer.
(b). How likely is the event that the maximum capacity of the lift will be exceeded when 16 persons enter the lift? Here I have use the central limit theorum and i get -26 as the answer, as you can see this is wrong.Can someone please help me figure this out?
(c). Should the sign on the lift be changed if acceptable risk of exceeding the maximum capacity, given that 16 persons enter the lift, is 20%?
To answer part (a) of the question, you correctly used the formula for standard error. The standard error of the mean (SE) is calculated by dividing the standard deviation (SD) by the square root of the sample size (n):
SE = SD / √n
In this case, the given SD is 8 kg and the sample size (n) is 16. Plugging these values into the formula, you should get the correct answer for the standard error.
For part (b), you need to calculate the probability of the maximum capacity being exceeded when 16 persons enter the lift. To do this, you can use the concept of the standard normal distribution and Z-scores.
First, you need to calculate the Z-score, which measures the number of standard deviations a particular value (in this case, the maximum capacity) is away from the mean. The formula for calculating the Z-score is:
Z = (X - μ) / σ
Where X is the maximum capacity, μ is the mean, and σ is the standard deviation. In this case, X = 1120 kg, μ = 68 kg, and σ = 8 kg.
Once you calculate the Z-score, you can find the corresponding probability using a Z-table or statistical software. The probability of exceeding the maximum capacity can be calculated as 1 minus the probability of being below the maximum capacity:
P(X > 1120) = 1 - P(Z < Z-score)
The Z-score you calculated should be positive, as it represents the number of standard deviations above the mean. Take the absolute value of this Z-score when looking it up in the Z-table.
For part (c), you need to compare the probability you calculated in part (b) with the acceptable risk level of 20%. If the probability of exceeding the maximum capacity is higher than 20%, it means there is an unacceptable risk. On the other hand, if the probability is lower than 20%, it means the risk is within the acceptable range.
For part (b) and (c), it's important to note that you need to use the correct Z-score and probability calculations to determine the likelihood and risk. Double-check your calculations and ensure you're referencing the Z-table correctly to calculate the probabilities.