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The birth weights of newborn elephants are normally distributed with a mean of 160 pounds and a standard deviation of 12 pounds.

What is the weight of the newborn elephant at the 33rd percentile?

Round to the nearest whole number.

A. 145 lbs
B. 175 lbs
C. 165 lbs
D. 155 lbs

Answer :

The weight of the newborn elephant at the 33rd percentile is approximately 155 lbs. Rounding to the nearest whole number, the weight of the newborn elephant at the 33rd percentile is approximately 155 lbs.

Find the z-score corresponding to the 33rd percentile using the formula: z = (X - μ) / σ, where X is the value we're looking for, μ is the mean (160 lbs), and σ is the standard deviation (12 lbs).

Plug in the values and solve for X: z = (X - 160) / 12

Rearrange the formula to solve for X: X = z * 12 + 160

Using a standard normal distribution table or calculator, find the z-score that corresponds to the 33rd percentile. The z-score is approximately -0.44.

Plug the z-score back into the formula: X = -0.44 * 12 + 160 = 155.32 lbs.

Rounding to the nearest whole number, the weight of the newborn elephant at the 33rd percentile is approximately 155 lbs.

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