Answer :
The observation for which 672 weights are smaller can be found by using the concept of the standard normal distribution.
To find this observation, we need to convert the given data into a standard normal distribution.
Step 1: Calculate the standard deviation. Since variance is given, we need to take the square root of the variance to find the standard deviation.
Standard deviation (σ) = √9 = 3 kgs
Step 2: Calculate the z-score for the desired observation. The z-score measures the number of standard deviations a data point is from the mean.
z-score = (observation - mean) / standard deviation
Let's denote the desired observation as x. Given that 672 weights are smaller, this observation is below 672 out of 4200, which means it falls below approximately 0.16 of the distribution.
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to a cumulative probability of 0.16. The z-score is approximately -0.9938.
Therefore, -0.9938 = (x - 70) / 3
Step 3: Solve for the observation (x).
Multiply both sides of the equation by 3:
-2.9814 = x - 70
Add 70 to both sides of the equation:
x = 67.0186
Therefore, the observation for which 672 weights are smaller is approximately 67 kgs.
So, the correct answer is a. 67.
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