The mean weight of the contents of samples of 30 bags of sugar has
standard error 0.008kg. Choose the option that is closest to the
probability, to three decimal places, that the mean weight of the
contents of samples of 30 bags of sugar will be 1kg or more.
Options for Question
A 0.700 B 0.800 C 0.824
D 0.858 E 0.887 F 0.932
You have to tell us what the mean weight is supposed to be. Suppose they are five pound bags!
I think you have omitted important data.
Sorry for that.
its 1.0042 kg
To determine the probability that the mean weight of the contents of samples of 30 bags of sugar will be 1kg or more, you can use the concept of the standard error and the normal distribution.
1. Calculate the Z-score: The Z-score measures how many standard errors a particular value is away from the mean. In this case, the mean weight is 1kg, and the standard error is 0.008kg. Thus, the Z-score can be calculated as follows:
Z = (1kg - mean weight) / standard error
Z = (1kg - mean weight) / 0.008kg
2. Use the Z-score to find the corresponding probability: Once you have the Z-score, you can use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) to find the probability corresponding to that Z-score.
Using a standard normal distribution table or calculator, you can look up the Z-score and find the corresponding probability.
Based on the given options, you need to find the probability closest to the answer.
Calculating the Z-score:
Z = (1kg - mean weight) / 0.008kg
Z = (1kg - mean weight) / 0.008kg
Z = (1 - mean weight) / 0.008
Since the actual value of the mean weight is not given, we cannot calculate the exact Z-score and probability. However, we can still compare the options to make the closest estimation based on the Z-score calculated.
Comparing the options:
Since we cannot calculate the exact probability without the mean weight value, we can compare the Z-score calculated to the Z-scores in the standard normal distribution table for each option to estimate the closest probability. Look for the Z-score closest to the calculated Z-score, and choose the corresponding option.
For example:
Z-score calculated = 1.2 (assume)
Comparing to the options, we see that Option C has the closest Z-score to 1.2. Therefore, the closest estimation for the probability is Option C: 0.824 to three decimal places.
Note: The exact probability value can only be determined with the actual mean weight value. Without that information, we can only estimate the closest probability based on the given options.