Question

A casino in Las Vegas, reporting to city officials, states that 34% of all gamblers at their facility end up winning money. The city officials take a random sample of 150 gamblers to test the casino's claims. With a 60% chance, the officials' sample proportion will be no greater than what value of p^? Round your answer to the nearest hundredth.

z score=
∅p∧=
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Answer 1

Using the given information that 34% of all gamblers win money, we can calculate the value of p^ is 0.41.

Step-by-step explanation:

To find the value of p^, we need to calculate the sample proportion of gamblers who end up winning money.

The officials took a sample of 150 gamblers, so we can use the formula:

p^ = number of gamblers who won / total sample size

Using the given information that 34% of all gamblers win money, we have:

p^ = 0.34 * 150

= 51

Now we can calculate the chance that the sample proportion is no greater than p^:

z score = (p^ - p) / sqrt(p*(1-p)/n)

Using p = 0.34, n = 150, and a 60% chance, we can rearrange the formula to solve for p^:

p^ = p + z * sqrt(p*(1-p)/n)

Plugging in the values, we get:

p^ = 0.34 + 0.60 * sqrt(0.34*(1-0.34)/150)

= 0.41

Therefore, the value of p^ rounded to the nearest hundredth is 0.41.