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 2
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 standard error and assume that the weights are normally distributed.
First, we need to find the Z-score corresponding to a mean weight of 1kg. The Z-score formula is given by:
Z = (X - μ) / SE
where X is the value of interest (1kg in this case), μ is the population mean, and SE is the standard error.
In this case, the population mean is not given, so we need to assume it is 1kg since we are interested in the probability of the mean weight being 1kg or more.
Therefore, the Z-score can be calculated as:
Z = (1 - 1) / 0.008 = 0 / 0.008 = 0
Now, we need to find the probability of Z being equal to or greater than 0. Using a standard normal distribution table or a statistical calculator, we can find that the probability is 0.500.
However, since we are interested in the probability of the mean weight being 1kg or more, we need to find the probability of Z being less than 0 and subtract it from 1.
P(Z < 0) = 0.500
P(Z >= 0) = 1 - P(Z < 0) = 1 - 0.500 = 0.500
Therefore, the probability that the mean weight of the contents of samples of 30 bags of sugar will be 1kg or more is 0.500.
None of the given options (A, B, C, D, E, F) match this probability exactly to three decimal places.