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

To find the probability that the mean weight of the contents of samples of 30 bags of sugar will be 1kg or more, we need to use the standard error and the mean weight.

The standard error is given as 0.008kg. This tells us the average amount of error we can expect in our estimates of the mean weight.

To find the probability, we need to convert the mean weight of 1kg into a z-score. The z-score is a measure of how many standard errors away from the mean the value is.

The formula to calculate the z-score is:

z = (x - μ) / σ

where x is the value we want to convert to a z-score, μ is the mean, and σ is the standard error.

In this case, x = 1kg, μ = 1.0042kg, and σ = 0.008kg.

Calculating the z-score:

z = (1 - 1.0042) / 0.008
z = -0.0042 / 0.008
z = -0.525

Now, we need to find the probability that the z-score is greater than or equal to -0.525. We can use a standard normal distribution table or a calculator to find this probability.

Using a standard normal distribution table, we can look up the area to the left of -0.525, which gives us the probability of the z-score being less than -0.525. To find the probability of the z-score being greater than or equal to -0.525, we subtract this probability from 1.

Looking up the area to the left of -0.525 in the table, we find that it is approximately 0.300. Subtracting this from 1 gives us:

1 - 0.300 = 0.700

Therefore, the closest option 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.