Q) The age for COVID-19 patients in a country is normally distributed with mean 57.6 years and standard deviation 28 years. A COVID-19 patient was randomly selected from that country. Find the probability that this patient
(i) is below 50 years.
(ii) is between 30 and 75 years.
(iii) 5% of the patients are above k years old. Find k.
(b) The number of COVID-19 patients in 5 different countries are shown in the table below.

Country A B C D E

Number of patients 1006 112 1104 926 1852 Test at 10% significance level, if the number of COVID-19 patients is evenly distributed among the five countries.

(c) In 2019, 20% of the students at University X are from China. In a random sample of 500 university students selected recently, it is found that that 130 of them are from China. Test if there is an increase in the percentage of China students in University X at 3% significance level

The age for COVID-19 patients in a country is normally distributed with mean 57.6 years and standard deviation 28 years. A COVID-19 patient was randomly selected from that country. Find the probability that this patient
(i) is below 50 years.
(ii) is between 30 and 75 years.
(iii) 5% of the patients are above k years old. Find k.
(b) The number of COVID-19 patients in 5 different countries are shown in the table below.
Country A B C D E Number of patients 1006 112 1104 926 1852 Test at 10% significance level, if the number of COVID-19 patients is evenly distributed among the five countries.

(c) In 2019, 20% of the students at University X are from China. In a random sample of 500 university students selected recently, it is found that that 130 of them are from China. Test if there is an increase in the percentage of China students in University X at 3% significance level.

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

It is estimated that 3.5% of the general population will live past their 90th birthday. In a graduating class of 759 high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday


(b) 30 or more will live beyond their 90th birthday


(c) between 25 and 35 will live beyond their 90th birthday


(d) more than 40 will live beyond their 90th birthday

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Ocean fishing for billfish is very popular in the Cozumel region of Mexico. In the Cozumel region about 47% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 27 strikes. Find the following probabilities. (Round your answers to four decimal places.)

ASK YOUR TEACHER

Based on long experience, an airline found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 263 ticket reservations for an airplane with only 255 seats.(a) What is the probability that a person holding a reservation will show up for the flight?


(b) Let n = 263 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows up holding a reservation?

P(r ≥ 263)P(r ≤ 263)    P(r ≥ 255)P(r ≤ 255

(c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)

One environmental group did a study of recycling habits in a California community. It found that 74% of the aluminum cans sold in the area were recycled. (Use the normal approximation. Round your answers to four decimal places.)

(a) If 384 cans are sold today, what is the probability that 300 or more will be recycled?


(b) Of the 384 cans sold, what is the probability that between 260 and 300 will be recycled?

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 220 customers on the number of hours cars are parked and the amount they are charged. Number of Hours Frequency Amount Charged 1 15 $ 2 2 36 6 3 53 9 4 40 13 5 20 14 6 11 16 7 9 18 8 36 22 220 Click here for the Excel Data File a-1. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round the intermediate calculations. Round your final answer to 3 decimal places.)

c-1 Find the mean and the standard deviation of the amount charged. (Do not round the intermediate calculations. Round your final answers to 3 decimal places.)

Consider the next 1000 90% CIs for ? that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of ?


What is the probability that between 890 and 910 of these intervals contain the corresponding value of ? [Hint: Let Y = the number among the 1000 intervals that contain ?. What kind of random variable is Y?] (Round your answer to four decimal places.)

Q1. Arrival of customers to a local store may be modeled by a Poisson process with an average of 1 arrival every 10 min period. Each customer on average stays for a time exponentially distributed with mean 15 minutes. This is modeled as a birth-death process.

(i) What assumption is necessary for this process to be modeled as a birth-death process?

(ii) Compute the probability that the number of customers in the store reaches 30, if we have 3 customers at the start.

Pls explain with workings. Thxs

Topten is a leading source on energy-efficient products. Their list of the top seven vehicles in terms of fuel efficiency for 2014 includes three Hondas.

1. Determine the probability distribution for the number of Hondas in a sample of two cars chosen from the top seven. (Round your answers to 4 decimal places.)

2. 	X P(X) 0 1 2 3

2. What is the likelihood that in the sample of two at least one Honda is included? (Round your answer to 4 decimal places.)

An article in Parenting magazine reported that 35% of Americans needed a vacation after visiting their families for the holidays. Suppose this is the true proportion of Americans who feel this way. A random sample of 200 Americans is taken. Let X be the number of people who feel that way in this random sample.

a) What is the mean of X?

b) Using the normal approximation, what is the probability that more than 80 people in the sample feel that they need a vacation after visiting their families for the holidays? (Round to 4 decimal places.)

Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample of 81 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.31 and 0.48? Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations. Answer = (Enter your answer as a number accurate to 4 decimal places.)