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 calculate 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 assume a normal distribution.
1. Determine the z-score: The z-score is calculated by subtracting the desired mean (1kg) from the actual mean and dividing by the standard error. In this case, the actual mean is not given, but we can assume it is 0 (since the standard error is measured from the mean). So the z-score would be (1 - 0) / 0.008 = 125.
2. Find the probability: Looking up the z-score of 125 in a standard normal distribution table, we see that the probability is very close to 1. In fact, it is practically 1.
Therefore, the option closest to the probability is option F: 0.932.