At a certain university, 50% of all entering freshmen planned to major in a STEM (science, technology, engineering, mathematics) discipline. A sample of 36 freshmen is selected. What is the probability that the proportion of freshmen in the sample is between 0.482 and 0.580? Write the answer as a number to the 4th decimal (0.1234).

The intended steps are as follows:

Step 1: Check to see that the conditions np ≥ 10 and n(1− p) ≥ 10 are
both met. If so, it is appropriate to use the normal curve.
Step 2: Find the mean U_p and standard deviation a_p.
Step 3: Sketch a normal curve and shade in the area to be found.
Step 4: Find the area using the TI-84 PLUS.

Employees of Harvin & Co. are divided among the three divisons: Management and Administration, Machine Operations, and Maintenance. The following table shows the number of employees in each division, classified by gender.

                                                    Female           Male           Total

Mgmt & Administration           20                   11                   31

Machine Operators                    75                 125                 200

Maintenance                                  4                   16                    20

Total                                            99                 152                  251

Let A = a randomly chosen employee is a female,

      B = a randomly chosen employee is a male,

      C = a randomly chosen employee works in Management & Administration,

      D = a randomly chosen employee is a machine operator.

What is the approximate probability that a randomly chosen employee is a machine operator given that this person is a female?   

Walthman Industries Inc. employs seven salespersons to sell and distribute its product throughout the state. Data taken from reports received from the salespersons during the year ended December 31 are as follows:

Required:

1. Prepare a table indicating contribution margin, variable cost of goods sold as a percent of sales, variable selling expenses as a percent of sales, and contribution margin ratio by salesperson. Round percents to the nearest whole number. Enter all amounts as positive numbers.

Feedback

Calculate:

Column 1: Contribution margin = Total sales – (Variable cost of goods sold + Variable selling expenses)

Column 2: Variable cost of goods sold as a percent of sales = Variable cost of goods sold/Total sales

Column 3: Variable selling expenses as a percent of sales = Variable selling expenses/Total sales

Column 4: Contribution margin ratio = Contribution margin/Total sales

2. Which salesperson generated the highest contribution margin ratio for the year?

Feedback

2. The salesperson who generated the highest contribution margin ratio for the year, probably sells a favorable mix of product that has high manufacturing margins as a percent of sales.

3. Identify the factors other than contribution margin that should be considered in evaluating the performance of salespersons.

1. Rate of growth in sales for the current year compared with past years
2. Years of experience for salespersons
3. Size of sales territory
4. Actual sales compared with budgeted sales
5. All of the above

Part A) Find the pressure in mmHg of a 0.124 g sample of helium gas in a 649 mL container at 34 ∘C. Express the pressure to three significant figures and include the appropriate units.

Part B) xture with a total pressure of 770 mmHg contains each of the following gases at the indicated partial pressures: 140 mmHg CO2, 112 mmHg Ar, and 128 mmHg O2. The mixture also contains helium gas.

What is the partial pressure of the helium gas?

What mass of helium gas is present in a 23.0-L sample of this mixture at 263 K ?

Part C)  cylinder with a moveable piston contains 0.76 mol of gas and has a volume of 337 mL .

What is its volume after an additional 0.26 mol of gas is added to the cylinder? (Assume constant temperature and pressure.)

Express your answer to three significant figures.

Part D) A gas mixture with a total pressure of 770 mmHg contains each of the following gases at the indicated partial pressures: 140 mmHg CO2, 112 mmHg Ar, and 128 mmHg O2. The mixture also contains helium gas.

What mass of helium gas is present in a 23.0-L sample of this mixture at 263 K ?

Express your answer in grams.

3. a) Using only the following information:   

• ∆H°f for NO (g) is +90.4 kJ/mol
   • ∆H° = –56.6 kJ/mol for the reaction: NO (g) + 1/2 O2 (g) à  NO2 (g)  

Determine ∆H°f for NO2 (g).

b) Using only your answer to (a) and the following information:    

•∆H° = –283.0 kJ/mol for the reaction: CO (g) + 1/2 O2 (g) à  CO2 (g)  Determine ∆H° for the reaction:   4 CO (g) + 2 NO2 (g) à  4 CO2 (g) + N2 (g)

c) A 10.0-L vessel contains 5.0 atm of CO and 3.0 atm of NO2 at 25°C. How much heat (in Joules) will be liberated if this is allowed to react to completion according to the reaction in part (b)?
d) In a separate experiment using a very large reaction vessel with a movable piston, 6.00 moles of CO2 (g) reacts completely with 3.00 moles of nitrogen gas according to the following equation at 25°C and with

a constant external pressure of 2.00 atm:

4 CO2 (g) + N2 (g) à  4 CO (g) + 2 NO2 (g)     
  This reaction proceeds to completion. Calculate ∆U, q, and w for this reaction under these conditions.

A commercial jet aircraft has two engines. Both engines have a reliability of 0.90, in other words the probability that a given engine will not fail is 0.90. Engines are assumed to operate independently from each other.

a. Do you think the following two events are mutually exclusive?

Event 1: Engine 1 will not fail
Event 2: Engine 2 will not fail

A) Yes, since they are independent

B) No

C) There is not enough information to determine if they are

D)Yes, since they are dependent   

b.What is the probability that both engines will fail?

c.Given that the second engine has failed, what is the probability that the first engine will fail?

d. Given that the first engine has failed, what is the probability that the second engine will fail?

e.What is the probability that neither engine will fail?

f.What is the probability that at least one of the engines will fail?

g.What is the probability that exactly one engine will fail?

STAT 14_3:

Ronit has a box with beads. The beads are opaque or transparent and available in several colors.
The probability of a random bead being red is 0.3. The probability of a bead being transparent is 0.6.
Of the red beads - the probability of a random bead being transparent is 0.5.

a. Remove 8 beads from the box at random and upon return. What is the probability that exactly two of them will be red?

b. Take beads out of the box accidentally and on return until you first remove a transparent bead
i. What is the probability of getting more than 4 beads?
ii. The first two beads taken out were not transparent. What is the probability of getting 7 beads out of the box?

c. Remove 10 beads from the box at random and upon return. What is the probability that exactly three of them will be red and transparent, two opaque and red and 5 transparent and red?

The reading speed of sixth-grade students is approximately normal with a mean speed of 125 words per minute and a standard deviation of 24 words per minute.
(Note: Labelled diagrams and proper notation are required for part a), b), c).)
a) What is the probability that a randomly selected student will read more than 130 words per minute? Interpret this probability.
b) What is the probability that the mean reading rate for a random sample of 12 sixth-grade students is more than 130 words per minute? Interpret this probability.
c) What is the probability that the mean reading rate for a random sample of 24 sixth-grade students is more than 130 words per minute? Interpret this probability.
d) Compare the probabilities in part b) and part c). What effect does increasing the sample size have on the probability?