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 for reading.
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 standard normal distribution.
1. Find the z-score: The z-score measures the number of standard deviations a particular value is from the mean. In this case, we want to find the z-score for the value 1kg. The formula for calculating the z-score is:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value we're interested in (1kg)
- μ is the mean weight (1.0042kg)
- σ is the standard error (0.008kg)
Substituting the values into the formula:
z = (1 - 1.0042) / 0.008
2. Look up the z-score in the standard normal distribution table: The z-score is used to find the corresponding area under the standard normal curve, which represents the probability. We need to find the probability of getting a z-score greater than the one calculated in the previous step.
Looking up the z-score in the standard normal distribution table, we find that the z-score corresponds to a probability of approximately 0.3159. This means that the probability of getting a mean weight of 1kg or more is approximately 0.3159.
3. Choose the closest option: Among the given options (A, B, C, D, E, F), we can see that the option closest to 0.3159 is option D: 0.858.
Thus, the closest 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 0.858.