Question

Jumbo eggs in Australia, on average, are supposed to weigh 68g. Margot is in charge of a quality control test that involves weighing a sample of eggs to see if if the sample mean weight is significantly different than 68g. She takes a random sample of 100 eggs and finds a mean weight of 67g and a sample standard deviation of 1g.

Required:
What is the probability that the mean weight of 4 eggs in a package is less than 68.5g?

Answer 1

To find the probability that the mean weight of 4 eggs in a package is less than 68.5g, we need to use the concept of sampling distribution.

Step-by-step explanation:

To find the probability that the mean weight of 4 eggs in a package is less than 68.5g, we need to use the concept of sampling distribution.

1. Step 1: Calculate the standard error of the mean using the formula: standard error = sample standard deviation / sqrt(sample size)
2. Step 2: Calculate the z-score using the formula: z = (sample mean - population mean) / standard error
3. Step 3: Use the z-score to find the probability using a z-table or calculator.

In this case, the sample mean is 67g, the sample standard deviation is 1g, and the population mean is 68g. Substituting these values into the formulas, we can calculate the probability that the mean weight of 4 eggs in a package is less than 68.5g.

Answer 2

-10

Step-by-step explanation:

Khan