The grade point averages​ (GPA) for 12 randomly selected college students are shown on the right. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed.

2.2 3.4 2.9 1.8 0.8 4.0 2.4 1.3 3.9 0.5 2.4 3.3 ​

(a) Find the sample mean.

x = _____ ​(Round to two decimal places as​ needed.) ​

(b) Find the sample standard deviation.

s= ______ (Round to two decimal places as​ needed.)

​(c) Construct a 95​% confidence interval for the population mean mu.

A 95​% confidence interval for the population mean is( ____, ____ ) . ​(Round to two decimal places as​ needed.)

A thin circular sheet of glass with a diameter 5 meters is rubbed with a cloth on one surface and becomes charged uniformly. A chloride ion (a chlorine atom which has gained one extra electron) passes near the glass sheet. When the chloride ion is near the center of the sheet, at a location 0.8 mm from the sheet, it experiences an electric force of 8e-15 N, toward the glass sheet. In this problem, use the value ε₀ = 8.85e-12 C²/(N·m²)

How much charge is on the surface of the glass disk? (give amount, including sign, and correct units)

Coal is carried from a mine in West Virginia to a power plant in New York in hopper
cars on a long train. The automatic hopper car loader is set to put 75 tons of coal into
each car. The actual weights of coal loaded into each car are normally distributed, with
mean μ = 75 tons and standard deviation σ = 0.8 ton.

(a) What is the probability that one car chosen at random will have less than 74.5 tons
of coal?

(b) What is the probability that 20 cars chosen at random will have a mean load weight
of less than 74.5 tons of coal?

The daily rainfall in Japan (measured in millimeters) is modelled using a gamma distribution with parameters α = 0.8 and β = 0.4.

Consider the overall rainfall in 365 days, and use mgfs and their properties to prove that this is Ga (292, 0.4).

1. Use the central limit theorem to approximate the probability that the annual rainfall exceeds 800mm (write down the analytical formula and the code used to calculate the cdf value).

2. Compare the approximate value obtained with the exact counterpart (include the R code used to calculate the cdf value).

3. Use R to produce a graphical representation that compares the true and approximate densities (include both the code and plot).

Sickle cell anemia is a recessive disorder caused by a mutation in the hemoglobin A gene. Persons with the disease have a variety of serious health issues related to fragile and sickling red blood cells including premature death, and infants sometimes die from complications. In regions of central Africa where malaria is endemic, the relative fitnesses for individuals that are homozygous for the wild type hemoglobin allele (Hb^A), heterozygous (Hb^AHb^S), and homozygous for the sickle cell allele (Hb^S) are 0.8, 1.0 and 0.1 respectively. The selection coefficient for someone of Central African ancestry who is an Hb^A/Hb^A homozygote born and raised in Chicago would be ____

This question relates to standing waves.

A) Does a closed pipe have a higher or lower fundamental frequency than an open pipe of the same length?

B) If the length of an open tube is 0.8 m, experimentally find the: fundamental frequency and the frequencies of the third and fifth harmonic.

C) We have only addressed the variables of length, wave speed, harmonic number and frequency. These seem to be adequate to fully describe the frequency of a standing wave. But we know that when a musician tightens a guitar string, the frequency of the sound changes. Which of these independent variables changes value when a string is tightened?

1. First, an object 1 with mass m and an object 2 with mass 2 m are moving on a straight line at velocities v1i = 1.00 m / s and v2i = -2.00 m / s. Two objects collided inelastically, and the velocities of object 1 and object 2 changed to v1f and vf2, respectively. The velocity is positive in the right direction, and no external force is acting on these two objects. Find v1f and vf2 for cases (1) and (2) below, respectively.
(1) When two objects have a completely inelastic collision.
(2) When two objects have a rebound coefficient e = 0.8.

-What is Purchasing power parity (PPP)?

2-When are currencies overvalued or undervalued?
3-How is the PPP calculated?
4-Why is the PPP important in international business?
5-Using the data below,

a) Find the implied PPP for the Euro Area,

b) Is the Euro under or overvalued against the dollar? and by how much? (must show your calculations for credit)

Big Mac Price USA: $5.28
Big Mac Price EU: 3.95 €