The mean weight (1.0042kg) 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
Thanks for reading.
To find the probability that the mean weight of the contents of samples of 30 bags of sugar will be 1kg or more, we can use the concept of the standard error.
The standard error measures the variability or uncertainty in the sample mean. It is calculated by dividing the standard deviation of the population by the square root of the sample size.
In this case, we know that the standard error is 0.008kg.
To find the probability that the mean weight is 1kg or more, we need to convert the mean weight of the sample to a z-score.
The formula for calculating the z-score is:
z = (x - μ) / SE
Where:
- x is the sample mean weight
- μ is the population mean weight
- SE is the standard error
In this case, the population mean weight is given as 1.0042kg and the sample mean weight we are interested in is 1kg.
Plugging in the values, we get:
z = (1 - 1.0042) / 0.008 = -0.525
Once we have the z-score, we can look up the corresponding probability in a standard normal distribution table. Since we are interested in the probability that the mean weight is 1kg or more, we need to find the area under the curve to the right of the z-score of -0.525.
Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score of -0.525 or less is approximately 0.700.
Therefore, the option closest to the probability, to three decimal places, is A) 0.700.