Question

The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.

A
5
9
n(AUB)-[I
3
11
5
14
B
Q

Answer 1

Explanation:

Calculate the population proportion of surgeons (p) from the given information:

p = 52% = 0.52

Calculate the population standard deviation (σ) for a sample proportion using the formula:

σ = √[p(1 - p) / n]

Where:

p is the population proportion.

n is the sample size.

σ = √[0.52 * (1 - 0.52) / 808]

σ ≈ √[0.2496 / 808]

σ ≈ √0.00030940594

σ ≈ 0.01759166

Calculate the Z-score for a sample proportion of 54%:

Z = (Sample proportion - Population proportion) / σ

Z = (0.54 - 0.52) / 0.01759166

Z ≈ 0.02 / 0.01759166

Z ≈ 1.1362

Find the probability that the sample proportion is greater than 54% by looking up the Z-score in a standard normal distribution table or by using a calculator or software. You want to find P(Z > 1.1362).

Using a standard normal distribution table or calculator, you can find that P(Z > 1.1362) is approximately 0.1271