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If the weights of students at U.O.J. are bell-shaped, we take a sample of 4200 students with a mean of 70 kg and a variance of 9 kg. Find the weight for which 2100 students are smaller.

Select one:
A. 70 kg
B. 64 kg
C. 67 kg
D. 73 kg

Answer :

Final answer:

The correct option is (a).The weight for which 2100 students are smaller is significantly larger than 70 kgs.

Explanation:

To find the weight for which 2100 students are smaller, we need to convert this number to a z-score. The z-score formula is:

z = (x - mean) / standard deviation

First, let's calculate the standard deviation. The variance given is 9 kgs, so the standard deviation is the square root of the variance:

standard deviation = sqrt(variance) = sqrt(9) = 3 kgs

Now, we can calculate the z-score:

z = (2100 - mean) / standard deviation = (2100 - 70) / 3

Simplifying the equation:

z = 2030 / 3 = 676.67

Next, we need to find the corresponding weight for this z-score using the standard normal distribution table. Looking up the z-score of 676.67 in the table, we find that it is beyond the range of the table. This means that the weight for which 2100 students are smaller is significantly larger than the mean weight of 70 kgs.

Therefore, none of the given options (a. 70, b. 64, c. 67, d. 73) is the correct answer.

Learn more about standard deviation here:

https://brainly.com/question/475676

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