1 New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night. Assume that room rates are 1 normally distributed with a standard deviation of $55.

a) What is the probability that a hotel room costs between $200 and $300 per night?

b) What is the cost of the 20% most expensive hotel rooms in New York City?

2 It is said that the New York City mobster Casper Holstein took as many as 25,000 bets per day in the Prohibition era. That's 150,000 bets in a week if he takes Sunday off. Casper's mean winnings per bet are $0.40. His standard deviation for single bets is about $18.96.

a. What are the mean and standard deviation of Casper's average winnings on his 150,000 bets?

b. According to the central limit theorem, what is the approximate probability that Casper's average winnings per bet are between $0.30 and $0.50? After only a week, Casper can be pretty confident that his winnings will be quite close to $0.40 per bet.

3 For this question also Interpret the 90% confidence interval that you calculate.

I want more muscle.Many young men in North America and Europe (but not in Asia) tend to think they need more muscle to be attractive. One study presented 200 young American men with 100 images of men with various levels of muscle.Researchers measure level of muscle in kilograms per square meter (kg/m²) of fat-free body mass. Typical young men have about 20 kg/m². Each subject chose two images, one that represented his own level of body muscle and one that he thought represented "what women prefer." The mean gap between self-image and "what women prefer" was 2.35 kg/m².

Suppose that the "muscle gap" in the population of all young men has a Normal distribution with standard deviation 2.5 kg/m². Give a 90% confidence interval for the mean amount of muscle young men think they should add to be attractive to women. (They are wrong: women actually prefer a level close to that of typical men.)

4 Explaining confidence.A student reads that a recent poll finds that a 95% confidence interval for the mean ideal weight given by an adult American women is 139 21.3 pounds. Asked to explain the meaning of this interval, the student says, "95% of all adult American women would say that their ideal weight is between 137.7 and 140.3 pounds." Is the student right? Explain your answer.

6 Sulfur compounds cause "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of wine (g/L). The untrainednoses of consumers may be less sensitive, however. The DMS odor thresholds for 10 untrained students was 29.4 (g/L).

Assume that the odor threshold for untrained noses is Normally distributed with=7g/L. Is there evidence that the mean threshold for untrained tasters is greater than 25g/L?

Null and alternative hypothesis.

P-value

Conclusion