Question: Children Women 0 12,508 1 7473 2 11,290 3 7113 4 3761 5 1810 6 915 7 523 8 or more 772 Total 46,165…

Children Women 0 12,508 1 7473 2 11,290 3 7113 4 3761 5 1810 6 915 7 523 8 or more 772 Total 46,165

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Part 1 of 4

(a) What is the probability that a sampled woman has six children? Round your answer to four decimals.

The probability that a sampled woman has six children is

Part: 1 / 4

Part 2 of 4

(b) What is the probability that a sampled woman has fewer than four children? Round your answer to four decimals.

The probability that a sampled woman has fewer than four children is

Part: 2 / 4

Part 3 of 4

(c) Assume this is a simple random sample of U.S. women. Use the Empirical Method to estimate the probability that a woman has more than five children. Round your answer to four decimal places.

The probability that a woman has more than five children is approximately

Part: 3 / 4

Part 4 of 4

(d) Using a cutoff of 0.05, is it unusual for a woman to have no children?

Solution

(a) To find the probability that a sampled woman has six children: First, find the number of women with six children: 913. Next, find the total number of women: 46,165. Calculate the probability: \[ P(\text{six children}) = \frac{913}{46,165} \] \[ P(\text{six children}) \approx 0.0198 \] So, the probability is approximately 0.0198. (b) To find the probability that a sampled woman has fewer than four children: Add the number of women with 0, 1, 2, or 3 children: \[ 12,308 + 7,473 + 11,290 + 7,113 = 38,184 \] Calculate the probability: \[ P(\text{fewer than four children}) = \frac{38,184}{46,165} \] \[ P(\text{fewer than four children}) \approx 0.8273 \] So, the probability is approximately 0.8273. (c) To estimate the probability that a woman has more than five children: Add the number of women with 6, 7, or 8 or more children: \[ 913 + 523 + 772 = 2,208 \] Calculate the probability: \[ P(\text{more than five children}) = \frac{2,208}{46,165} \] \[ P(\text{more than five children}) \approx 0.0478 \] So, the probability is approximately 0.0478.