Consider eruptions of Old Faithful geyser in Yellowstone National Park. The distribution of eruptions is said to be roughly normal and based on a study done in the park in 2011 has a mean time between eruptions of 93 minutes with a standard deviation of 9.5 minutes.

A)Suppose we are still studying 60 eruptions and we want to know what the longest 5% of mean times between eruptions would be. What average time would put us in the longest 5%?

B)How would your previous answer change if we were only studying 20 eruptions?

C)If we study 45 eruptions, what is the chance that a mean eruption time would differ from the true mean by less than 5 minutes?

D)If we study 45 eruptions, what is the chance that a mean eruption time would differ from the true mean by less than 1 minute?

2. According to Newton’s Law of Cooling, the rate of change of the temperature of an object can be modeled using the following differential equation:

dT/dt = k(T-T_R)

where T is the temperature of the object (in ◦F), TR is the room temperature (in ◦F), and κ is the constant of proportionality.
On a crime show, the detective discovers a dead body in a hotel room.
(a) Write the differential equation to describe the change in temperature of the body if κ = −0.405 and thermostat in the hotel room is set at 70◦F.
(b) Solve the differential equation using an appropriate method. State the method you used and show your work.
(c) Assuming the victim was a healthy 98.6◦F at the time of the murder, we have the initial condition that T(0) = 98.6. Find the particular solution to the IVP.
(d) If the body temperature is 85◦F when the crime scene is discovered, how long has the victim been dead? (Assume t is measured in hours.)

1. Fossa (a terrestrial mammal in Madagascar) experience a population decline of 20% each time a cyclone hit a particular national park on the African coast, because their prey populations also decline rapidly. Usually, one cyclone hits every 10 years. However, in one unusual year, five cyclones hit this national park and the population was reduced in quick succession to a level that was then easily wiped out by hunters. The primary causes of this population’s extinction were:

a) Over-Exploitation & Demographic Stochasticity

b) Over-Exploitation & Environmental Stochasticity

c) Demographic Stochasticity & Habitat Loss

d) Environmental Stochasticity & Habitat Loss

e) Demographic & Environmental Stochasticity

2. For a decreasing population, which of the following could be true regarding a declining population?

) Braha Boda Hotel’s is a company in the hospitality industry that take care of travelers along its area of operation. The budgets for the Hotel got the year 2010 are as follows:

                                                         GHS                            GHS

Occupants Charges                                                          1,100,000

Costs:                 

Variable:

Direct supplies.                         80,000

Direct salaries                           600,000

Occupation service:

   Overheads                             65,000

   Administration.                     92,000

Fixed:

Overheads                               125,000

Administration                        140,000                         1,102,000

Loss                                                                                 (2,000)

Additional Information:

1. Number of rooms available        100 per day

2. Occupants days                         24,000 per annum

You are required to compute:

(i)   The contribution margin ratio.

(ii) The break-even point in both occupants’ days and occupants’ charges.

(iii) The margin of safety ratio if the Hotel operates at fully capacity.

(iv) The break-even points one occupants’ days of direct salary were

increased to GHS626,000.

(v) The break-even in occupants’ days if fixed occupants service overheads were increased to GHS145,000.

A survey found that​ women's heights are normally distributed with mean

62.1

in. and standard deviation

3.1 in. The survey also found that​ men's heights are normally distributed with mean 69.6 in. and standard deviation 3.7

in. Most of the live characters employed at an amusement park have height requirements of a minimum of

56 in. and a maximum of

63in. Complete parts​ (a) and​ (b) below.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​ park?

The percentage of men who meet the height requirement is

nothing​%.

​(Round to two decimal places as​ needed.)

Since most men

▼

meet

do not meet

the height​ requirement, it is likely that most of the characters are

▼

women.

men.

b. If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements?

The new height requirements are a minimum of nothing in. and a maximum of nothing in.

1.

A random sample of ten households in College Park revealed they generated a mean of 10.91 pounds of garbage per week with a standard deviation of 4.736 pounds. Construct the 80% confidence interval to estimate the mean amount of garbage all College Park households generate per week

8.1646 pounds to 13.6554 pounds

7.5220 pounds to 14.2980 pounds

8.8387 pounds to 12.9813 pounds

6.0429 pounds to 15.7771 pounds

2.

Suppose National Collegiate Athletic Association [NCAA] rules state all student-athletes are to receive an average of 50 hours of academic support, per term. A random sample of 49 University of Maryland student-athletes revealed a mean of 47.5 hours of academic support per term. If the calculated value for the associated test statistic equaled -1.75, what was the standard deviation of the number of hours of academic support the student-athletes in the sample received per term?

12

15

7

10

Taking the family to an amusement park has become increasingly costly according to the industry publication Amusement Business, which provides figures on the cost for a family of four to spend the day at one of America’s amusement parks. A random sample of 25 families of four that attended amusement parks yielded the following costs, rounded to the nearest dollar.

Given the cost is normally distributed.

a) Suppose the population standard deviation is $21. Determine a 95% confidence interval for the mean cost of a family of four to spend the day at an American amusement park.

c) What is the margin of error of the 95% confidence interval obtained ?

d) Suppose we want to find a 95% confidence interval with margin of error 0.5. How many samples shall we collect?   

Otay Lakes Park is a private camping ground near the Mount Miguel Recreation Area. It has compiled the following financial information as of December 31, 2017.

Instructions

(a)  

Determine Otay Lakes Park's net income for 2017.

(b)  

Prepare a retained earnings statement and a balance sheet for Otay Lakes Park as of December 31, 2017.

(c)  

Upon seeing this income statement, Walt Jones, the campground manager, immediately concluded, “The general store is more trouble than it is worth—let's get rid of it.” The marketing director isn't so sure this is a good idea. What do you think?