High School

Assume that women's weights are normally distributed with a mean of 143 lb and a standard deviation of 29 lb.

35 randomly selected women have a mean of 130 lb.

What is the z-score corresponding to the sample mean of 130 and sample size of 35?

1) -1.45
2) -1.96
3) -2.65
4) -1.65

Answer :

Final answer:

The z-score corresponding to a sample mean of 130 lbs. with a sample size of 35, when the the population mean is 143 lbs. and the standard deviation is 29 lbs., is approximately -1.65

Explanation:

To calculate the z-score corresponding to the sample mean, we use the formula for the z-score, which is (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

Substituting the values from the question into the formula, we find the z-score is (130 - 143) / (29 / √35) = -13 / (29 / √35) which gives us a z-score of roughly -1.65 (4th option), assuming that the population mean and standard deviation were 143 lbs. and 29 lbs. respectively, not the negative values.

Learn more about Z-score here:

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