Suppose a carnival director in a certain city imposes a height limit on an amusement park ride called Terror Mountain, due to safety concerns. Patrons must be at least 4 feet tall to ride Terror Mountain. Suppose patrons’ heights in this city follow a Normal distribution with a mean of 4.5 feet and a standard deviation of 0.8 feet (patrons are mostly children). Make sure to show all of your work in this question. Show the distribution that your random variable follows; state the probability you are asked to calculate; show any tricks you use; show how you standardize, and state your found value from Table A4.

a) [5 marks] What is the probability that a randomly selected patron would be tall enough to ride Terror Mountain?

b) [5 marks] A group of 3 friends want to ride Terror Mountain. What is the probability that their mean height is greater than 4.5 feet?

c) [7 marks] Another group of 5 friends wants to ride Terror Mountain. What is the probability that their mean height is between 4 and 4.25 feet, inclusive?

Jorge was at the park playing with friends. He found a typical die with 6 sides on the ground. He took it home and rolled it 100 times and recorded the results (found in the table below). He wanted to see if the die was a 'fair die' or if it was weighted on one side so somone could cheat when playing games!

Is this a 'fair die' or has it been tampered with? Test at the α=0.05 level of significance.

Which would be correct hypotheses for this test?

H0:μ1=μ2

; H1:μ1≠μ2
H0:
The die is a fair die; H1:
The die has been tampered with
H0:p1=p2
; H1:p1≠p2
H0:
The die has been tampered with; H1:

The die is a fair die

Roll count:

Rolled   Count
1   1
2   5
3   4
4   6
5   9
6   75

Test Statistic:

Give the P-value:

Which is the correct result:

Reject the Null Hypothesis
Do not Reject the Null Hypothesis

Which would be the appropriate conclusion?

There is enough evidence to suggest that the die has been tampered with.
There is not enough evidence to suggest that the die has been tampered with.

Adjusted WACC. ​ Hollydale's is a clothing store in East Park. It paid an annual dividend of ​$1.20 last year to its shareholders and plans to increase the dividend annually at 3.0​%. It has 590 comma 000 shares outstanding. The shares currently sell for ​$17.37 per share. ​ Hollydale's has 11 comma 000 semiannual bonds outstanding with a coupon rate of 6​%, a maturity of 24 ​years, and a par value of ​$1 comma 000. The bonds are currently selling for ​$638.46 per bond. What is the adjusted WACC for​ Hollydale's if the corporate tax rate is 40​%?

A new roller coaster at an amusement park requires individuals to be at least​ 4' 8"

​(56 inches) tall to ride. It is estimated that the heights of​ 10-year-old boys are normally distributed with

mu equals μ=55.0 inches and sigma equals σ=4 inches.

a. What proportion of​ 10-year-old boys is tall enough to ride the​ coaster?

b. A smaller coaster has a height requirement of

50 inches to ride. What proportion of​ 10-year-old boys is tall enough to ride this​ coaster?

c. What proportion of​ 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part​ a?

A pair of bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear, as seen in part (a) of the figure below. ((a) before collision, (b) after collision) One has a mass of m1 = 462 kg and the other m2 = 546 kg, owing to differences in passenger mass. If the lighter one approaches at v1 = 4.48 m/s and the other is moving at v2 = 3.63 m/s, calculate the velocity of the lighter car after the collision.

Calculate the velocity of the heavier car after the collision.

Calculate the change in momentum of the lighter car.

Calculate the change in momentum of the heavier car.

(a) Have you ever visited an amusement park and taken a ride on a parachute drop ride? These types of rides take the passengers to a great height, and then drop them in free fall. Before they hit the ground, the ride is slowed using a Lenz’s law mechanism thus avoiding certain death. For this discussion, first locate a photo of one of these rides (either one you’ve personally experienced or one you might like to try someday), and in your initial post, upload the photo and respond to the following:

• Explain how Lenz’s law applies to this situation.
• Why is the Lenz’s law mechanism ideal for such a use?
• What other mechanisms can be used to slow the descent? Compare and contrast these options with the Lenz’s law mechanism.

(b) As you have learned, an electromagnet is a magnet that is produced by electric current. Think about how electromagnets are used and what you have seen or heard of them being used for. In your initial discussion post, respond to the following:

• Which of the principles or laws discussed in this module explain how an electromagnet works?
• Describe in detail two modern applications of electromagnets. Do these electromagnets draw a large amount of current or a little? How do you know? What supplies that current?
• Why do you think electromagnets are used in these different ways?
• What is the advantage of using an electromagnet rather than a permanent magnet?

a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water flowing down it. Can the equation for conservation of mechanical energy be used on the child?

YesNo     

(b) Is the mass of the child a factor in determining his speed at the bottom of the slide?

YesNo     

(c) The child drops straight down rather than following the curved ramp of the slide. In which case will he be traveling faster at ground level?

following the curved rampdropping straight down     same speed in either case

(d) If friction is present, how would the conservation-of-energy equation be modified?


(e) Find the maximum speed of the child when the slide is frictionless if the initial height of the slide is 13.5 m. (Assume the child is initially at rest.)
m/s

Water Planet is considering purchasing a water park in Miami, Florida​, for $ 2,100,000. The new facility will generate annual net cash inflows of $ 535,000 for eight years. Engineers estimate that the facility will remain useful for eight years and have no residual value. The company uses​ straight-line depreciation. Its owners want payback in less than five years and an ARR of 10​% or more. Management uses a 12% hurdle rate on investments of this nature.

.

Requirement 1. Compute the payback​ period, the​ ARR, the​ NPV, and the approximate IRR of this investment.​ (If you use the tables to compute the​ IRR, answer with the closest interest rate shown in the​ tables.) ​(Round the payback period to one decimal​ place.)

​(Round the percentage to the nearest tenth​ percent.)

​(Round your answer to the nearest whole​ dollar.)

The IRR​ (internal rate of​ return) is between

.

Requirement 2. Recommend whether the company should invest in this project.

Detmer Liebold uses a job-order costing system with a single predetermined overhead rate based on direct labor hours. The predetermined overhead rate is based on the following data: Total direct labor hours 70,000

Total fixed overhead cost 273,000

Variable manufacturing overhead per direct labor hour $6.00

Job 924 was recently completed with the following characteristics.

Number of units produced 50

Total direct labor hours 100 Direct materials $680

Direct labor cost $7,000

Complete the following table to calculate the unit product cost for Job 924:

Account                                                                            Amount                                               Calculations

Total fixed manufacturing overhead cost

+ Total variable manufacturing overhead cost

Total manufacturing overhead cost

/ Direct labor hours

Predetermined overhead rate

Direct materials

Direct labor

Manufacturing overhead applied

Total cost of Job 924

Total cost of Job 924    From calculation above

/ Number of units produced Unit product cost for Job 924