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
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 and the normal distribution.
The standard error is a measure of how much the sample means vary from the population mean. In this case, the standard error is given as 0.008kg.
Since we are dealing with a sample mean, we can assume that the distribution of the sample means will follow a normal distribution.
To find the probability, we need to convert the value of 1kg into a z-score using the formula:
z = (X - μ) / σ,
where X is the value we want to convert, μ is the mean, and σ is the standard deviation.
In this case, since we are dealing with sample means, the mean μ would be the population mean, and the standard deviation σ would be the standard error (0.008kg).
Calculating the z-score:
z = (1 - μ) / σ = (1 - 0) / 0.008 = 125.
With this z-score, we can now find the probability using a standard normal distribution table or a calculator.
Looking up the closest z-score of 1.25 in the table or using a calculator, you will find that the corresponding probability is approximately 0.894.
Since this probability represents the probability that the mean weight of the contents of samples of 30 bags of sugar will be less than 1kg, we subtract it from 1 to find the probability that it will be 1kg or more:
1 - 0.894 = 0.106.
Therefore, the option closest to the probability, to three decimal places, is A 0.106.