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How many bags must be sampled so that the probability is 0.01 that the sample mean weight is less than 14 kg? Round the answer to the next largest whole number.

A. 265
B. 217
C. 142
D. 94

Answer :

the probability is 0.01 that the sample mean weight is less than 14 kg. Therefore, approximately 5 bags must be sampled.(Non of Option)

Here are the calculations:

Step 1: Determine the z-score corresponding to the desired probability (0.01). Since we are interested in the left tail of the distribution, we use a negative z-score. From the standard normal distribution table (or calculator), the z-score corresponding to a probability of 0.01 is approximately -2.33.

Step 2: Calculate the standard error of the mean (SEM) using the formula:

SEM = σ / √n

Given that the population standard deviation (σ) is 14 kg, we have:

SEM = 14 / √n

Step 3: Rearrange the z-score formula to solve for the sample size (n):

n = (z * σ / desired SEM)^2

Substitute the known values: z = -2.33, σ = 14 kg, and the desired SEM is 14 kg:

n = (-2.33 * 14 / 14)^2

n = (-32.62 / 14)^2

n = (-2.33)^2

n = 5.4289

Step 4: Round up to the next largest whole number to ensure that the probability is 0.01 that the sample mean weight is less than 14 kg. Therefore, approximately 5 bags must be sampled.(Non of Option)

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