Question

In: Math

Of all cities in the United States, Amherst, New York, has the fewest number of days...

Of all cities in the United States, Amherst, New York, has the fewest number of days per year clear of clouds, 4.4. Other cities with very few clear days include Buffalo, New York, Lakewood, Washington, and Seattle, Washington. Suppose a random year is selected. (Round your answers to four decimal places.)

(a)

What is the probability that Amherst will have exactly four days clear of clouds?

(b)

What is the probability of fewer than six days clear of clouds?

(c)

What is the probability of at least nine days clear of clouds?

(d)

Suppose that between 2 and 11 (inclusive) days are clear of clouds. What is the probability of more than five days clear of clouds?

this is all the data provided for this question.

Solutions

Expert Solution

Answer:

a)

Given,

= 4.4

Here we are utilizing poisson distribution

P(X = 4) = e^-4.4 * 4.4^4 / 4!

= 4.6888/24

P(X = 4) = 0.19174

Hence the probability that Amherst will have exactly four days clear of clouds is 0.19174

b)

To determine the probability of fewer than six days clear of clouds

P(X < 6) = e^-4.4*4.4^x / x!

= e^-4.4*4.4^0/0! + e^-4.4*4.4^1/1! + e^-4.4*4.4^2/2! + e^-4.4*4.4^3/3! + e^-4.4*4.4^4/4! + e^-4.4*4.4^5/5!

= 0.012277339 + 0.054020295 + 0.11884465 + 0.174305487 + 0.191736035 + 0.168727711

P(X < 6) = 0.7199

c)

To determine the probability of at least nine days clear of clouds

P(X >= 9) = 1 - P(X <= 8)

= 1 - [e^-4.4*4.4^0/0! + e^-4.4*4.4^1/1! + e^-4.4*4.4^2/2! + e^-4.4*4.4^3/3! + e^-4.4*4.4^4/4! + e^-4.4*4.4^5/5! + e^-4.4*4.4^6/6! + e^-4.4*4.4^7/7! + e^-4.4*4.4^8/8!]

= 1 - [ 0.012277339 + 0.054020295 + 0.11884465 + 0.174305487 + 0.191736035 + 0.168727711 + 0.123733655 + 0.07777544 + 0.042776492]

= 1 - [0.9642]

P(X >= 9) = 0.0358

d)

To give required probability

P(2 <= X <= 11) = e^-4.4 * 4.4^x / x!

On solving we get

= 0.9317

P(2 <= X <= 11) = 0.9317

milcah answered 1 year ago
Next > < Previous

Related Solutions

Leigh of New York sells its products to customers in the United States and the United...
Leigh of New York sells its products to customers in the United States and the United Kingdom. On December 16, 2017, Leigh sold merchandise on credit to Bronson Ltd. of London at a price of 18,000 pounds. The exchange rate on that day for £1 was $2.0235. On December 31, 2017, when Leigh prepared its financial statements, the rate was £1 for $2.0174. Bronson paid its bill in full on January 15, 2018, at which time the exchange rate was...
New York City is the most expensive city in the United States for lodging.
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55.what is the probability that a hotel room costs $225 or more per night?what is the probability that a hotel room costs less than $140 per night?What is the probability that a hotel room costs between $200 and $300 per...
New York City is the most expensive city in the United States for lodging.
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55. Use Table 1 in Appendix B. a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)? b. What is the probability that a hotel room costs less than $143 per night...
In New York, which has the largest ride-for-hire fleet in the United States, licenses have been...
In New York, which has the largest ride-for-hire fleet in the United States, licenses have been issued for 13,437 taxicabs. There are an estimated 42,000 drivers in the city, with a licensed vehicle being used by two or three drivers a day. In 2014, only 6% of cab drivers in New York were born in the United States, and 36% came from Bangladesh and Pakistan. The New York taxi fleet picks up 600,000 passengers per day. An estimated 25,000 livery...
New York City is the most expensive city in the United States for lodging. The mean...
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55. a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)? b. What is the probability that a hotel room costs less than $140 per night (to 4 decimals)? c. What is...
New York City is the most expensive city in the United States for lodging. The mean...
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 normally distributed with a standard deviation of $55. a. What is the probability that a hotel room costs $225 or more per night? b. What is the probability that a hotel room costs less than $140 per night? c. What is the probability that a hotel room costs between $200 and $300...
New York City is the most expensive city in the United States for lodging. The mean...
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55. Use Table 1 in Appendix B. a. What is the probability that a hotel room costs $227 or more per night (to 4 decimals)? b. What is the probability that a hotel room costs less than $143 per night...
New York City is the most expensive city in the United States for lodging. The mean...
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $53. Use Table 1 in Appendix B. a. What is the probability that a hotel room costs $224 or more per night (to 4 decimals)? b. What is the probability that a hotel room costs less than $139 per night...
New York City is the most expensive city in the United States for lodging. The mean...
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $203 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $56. Use Table 1 in Appendix B. a. What is the probability that a hotel room costs $227 or more per night (to 4 decimals)? b. What is the probability that a hotel room costs less than $139 per night...
From California to New York, legislative bodies across the United States are considering eliminating or reducing...
From California to New York, legislative bodies across the United States are considering eliminating or reducing the surcharges that banks impose on noncustomers, who make $14 million in withdrawals from other banks’ ATM machines. On average, noncustomers earn a wage of $24 per hour and pay ATM fees of $3.25 per transaction. It is estimated that banks would be willing to maintain services for 6 million transactions at $1.00 per transaction, while noncustomers would attempt to conduct 22 million transactions...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT