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 determine 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.
1. First, we need to calculate the z-score using the formula: z = (x - μ) / σ, where x is the threshold value (1kg in this case), μ is the mean weight (1.0042kg), and σ is the standard error (0.008kg).
Calculating the z-score: z = (1 - 1.0042) / 0.008 = -0.525.
2. Next, we find the corresponding cumulative probability using the z-score. We look up this value in the standard normal distribution table. In this case, we are interested in the probability to the right of the z-score since we want the mean weight to be 1kg or more.
Using the standard normal distribution table, the closest value to -0.525 is 0.700. This means that approximately 0.700 is the probability associated with a z-score of -0.525.
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.