Use the Empirical Rule to answer the questions below: The distribution of weight

Question

Use the Empirical Rule to answer the questions below: The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.5 pounds and a standard deviation of 0.7 pounds. I. What percent of newborn babies weigh more than 8.2 pounds? 2. The middle 95% of newborn babies weigh between 3. What percent of newborn babies weigh less than 6.1 pounds? 4. Approximately 50% of newborn babies weigh more than 5. What percent of newborn babies weigh between 6.8 and 9.6 pounds? % and pounds. pounds %

Explanation / Answer

Formula: Z = (x-mean)/SD

1. P(X > 8.2) = 1 - P(X < 8.2) = 1 - P(Z < (8.2-7.5)/0.7) = 1 - P(Z < 1) = 0.1587

2. P(X < x1) = 0.025, Z = -1.96
For x2, Z = 1.96

x1 = 6.128

x2 = 8.872

3. P(X < 6.1) = P(Z < (6.1-7.5)/0.7) = P(Z < -2) = 0.0228

4) For p =0.5, Z = 0

X = mean = 7.5

5) P(6.8 < X < 9.6) = P(X < 9.6) - P(X < 6.8) = P(Z < 3) - P(Z < -1) = 0.9987 - 0.1587 = 0.84

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