Question

Cruise Bermuda Ocean Adventure has been growing exponentially in the past few years, based on its business models of operating low-price cruises from Miami to Bermuda targeted solely to retirees in the 65-80 age range. While the average all-inclusive 7-day Caribbean cruise will cost between $499 and $1,499 (traveltips.usatoday.com), Cruise Bermuda’s all-inclusive 7-day Caribbean cruise averages just $350 per person. What’s more, Cruise Bermuda makes sure to only stop at the tourist sites that require little or no cost to enjoy, leading to Cruiseranker.Com (hypothetical website) naming Cruise Bermuda’s the best value Caribbean cruises on the market.

The executives at Cruise Bermuda need to keep current on their cost analysis and relevant customer statistics in order to remain financially viable while maintaining their status as the ‘best value on the market’. Here are some of the relevant data analyses that could be included in the statistical analysis activities that Cruise Bermuda may engage in…

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1. The distribution of annual household income (including annuities, pension, other retirement income, real estate income, social security, gifts from family, etc.) of Cruise Bermuda’s customers approximates a normal distribution with a mean of $47,200 and a standard deviation of $800.

a. About 68% of the incomes lie between what two amounts?

b. About 95% of the incomes lie between what two amounts?

c. Virtually all of the incomes lie between what two amounts?

d. What are the median and modal incomes?

e. Is the distribution of incomes symmetrical?

2. A survey done by the Bermuda Tourism Board reported that the average cruise ship visitor to Bermuda spends $185 for souvenirs and the like. Assume the distribution of visitor spending is uniform and described by the probability density function.

F(x) = {   1/50 for x values between $160 and $210

{ 0 everywhere else

…where x = values for the random variable “cruise ship visitor spending”.

a. What percentage of cruise ship visitors spend between $170 and $180?

b. What percentage of cruise ship visitors spend less than $165?

c. 70% of cruise ship visitors spend less than ____.

d. What is the standard deviation of the visitor spending distribution?

3. Records show that an average of 1.4 customers per hour check into the Sick Bay (medical care center) on board the ship (that is, ?= 1.4 check-ins per hour). Assume that Sick Bay customer check-ins meet all of the Poisson conditions:

a. How likely is it that less than a half-hour will elapse between one check-in and the next?

b. How likely is it that more than two hours will elapse between successive check-ins?

c. At a given time, how likely is it that no more than 20 minutes will elapse before the next check-in?

d. How likely is it that between 30 minutes and 45 minutes will elapse before the next sick customer checks in?

4. Surveys of customers show that distribution of total amount spent for a couple including cruise fee, tax, insurance and on-board extra spending follows a normal distribution with a mean of $1,000 and a standard deviation of $100.

a. What fraction of the couples spend between $750 and $1,225? Draw a normal curve and shade the desired area on your diagram.

b. What fraction of the couples spend between $1,100 and $1,225? Draw a normal curve and shade the desired area on your diagram.

c. What fraction of the couples spend less than $1,000? Draw a normal curve and shade the desired area on your diagram.

5. Write a brief conclusion about the implications of these statistics for Cruise Bermuda.

Answer 1

Let X denote the random variable representing annual household income (including annuities, pension, other retirement income, real estate income, social security, gifts from family, etc.) of Cruise Bermuda’s customers.

Mean of X, = $47,200

Standard deviation os X, = 800

a) About 68% of the incomes lie between what two amounts

z values for 68% = 1

C.I(68) = =  

About 68% of the incomes lie between (48000-46400)

b) About 95% of the incomes lie between what two amounts

z values for 95% = 1.96

C.I(95) = =  

About 95% of the incomes lie between (48768-45632)

c. Virtually all of the incomes lie between what two amounts?

z values for 99.7% = 3

C.I(95) = =  

About 95% of the incomes lie between (49600-44800)

d. What are the median and modal incomes?

Since the income approximates the normal distribution.

Mean, median and mode will have same value = $47200

e. Is the distribution of incomes symmetrical?

Yes, the distribution is symmetrical.

Please post rest of the questions as seperate questions.