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Chapter 6: Problem 90

Babies in the United States have a mean birth length of \(20.5\) inches with a standard deviation of \(0.90\) inch. The shape of the distribution of birth lengths is approximately Normal. a. Find the birth length at the \(2.5\) th percentile. b. Find the birth length at the \(97.5\) th percentile. c. Find the \(z\) -score for the length at the \(2.5\) th percentile. d. Find the \(z\) -score for the length at the \(97.5\) th percentile.

Short Answer

Expert verified
The birth length at the 2.5th percentile is approximately 18.74 inches and at the 97.5th percentile is approximately 22.26 inches. The Z-score for the length at the 2.5th percentile is -1.96 and at the 97.5th percentile is 1.96.

Step by step solution

01

Find the birth lengths at the given percentiles

To find the birth length at the 2.5th percentile: Use the Z-table to find the Z score that corresponds to the 2.5th percentile which is -1.96. Then, use the formula: Value = Mean + Z(SD), thus, Value = 20.5 + (-1.96 * 0.90). To find the birth length at the 97.5th percentile: Use the Z-table to find the Z score that corresponds to the 97.5th percentile which is 1.96. Then, use the formula: Value = Mean + Z(SD), thus, Value = 20.5 + (1.96 * 0.90)
02

Find Z-scores for the lengths at given percentiles

The Z-score for the length at the 2.5th percentile is -1.96, already given above. Similarly, the Z-score for the length at the 97.5th percentile is 1.96.

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Most popular questions from this chapter

According to National Vital Statistics, the average length of a newborn baby is \(19.5\) inches with a standard deviation of \(0.9\) inch. The distribution of lengths is approximately Normal. Use a table or technology for each question. Include an appropriately labeled and shaded Normal curve for each part. There should be three separate curves. an What is the probability that a baby will have a length of \(20.4\) inches or more? b. What is the probability that a baby will have a length of \(21.4\) inches or more? c. What is the probability that a baby will be between 18 and 21 inches in length?

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