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.
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.
Standard error measures the variability or uncertainty of the sample mean. It is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard error is given as 0.008kg.
To find the probability, we can use the z-score formula. The z-score measures how many standard errors a particular value is away from the mean. It is calculated by subtracting the mean from the value and dividing by the standard error.
In this case, we want to find the probability that the mean weight is 1kg or more. To do this, we need to convert 1kg to a z-score. Since the mean is given as 1.0042kg, the z-score is calculated as (1 - 1.0042) / 0.008.
z = (1 - 1.0042) / 0.008 = -0.525
We can then use a standard normal table or a calculator to find the probability corresponding to a z-score of -0.525. For this question, the options are given in the form of decimals or approximations.
Using a standard normal table or a calculator, we find that the closest probability to -0.525 is 0.700 (option A).
Therefore, the option 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 is option A - 0.700.