The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 3 minutes.

(a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?

b) Without assuming anything about the distribution of times, at least what percentage of the times are between 29 and 41 minutes? (Round the answer to the nearest whole number.)
At least   %

(c) Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 26 minutes or greater than 44 minutes? (Round the answer to the nearest whole number.)
No more than   %

(d) Assuming that the distribution of times is normal, about what percentage of times are between 29 and 41 minutes? (Round the answers to two decimal places, if needed.)
  %

Less than 26 min or greater than 44 min?
  %

Less than 26 min?
  %

A paper studied various aspects of bus service and presented data on travel times from several different routes. The accompanying frequency distribution is for bus travel times from origin to destination on one particular route in Chicago during peak morning traffic periods.

Compute (approximately) the percentiles. (Round your answers to one decimal place.)

1. Section 3.1 Measures of Central Tendency

pH in Water:

The acidity of alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water.

2. pH in Water:

Use the same pH data table in the above question to answer the following.

1. Which type of water has more dispersion in pH using the range as the measure of dispersion?
2. Which type of water has more dispersion in pH using the standard deviation as the measure of dispersion?

There are six blue balls and four red balls in the pocket. Take out a ball at random, check the color and put it back in the pocket.
1. If you take the ball out until the red one comes out, what is the probability that the ball will be drawn exactly five times and the experiment is over?
2. What is the average and variance of the number of times X is taken if the ball is pulled out until the red ball comes out?
3. Repeat the procedure ten times to remove the ball from the pocket. Find the mean and variance of the number of blue balls taken Y.

1. Section 3.4 Measures of Position and Outliers

You Explain it – Percentiles & Quartiles:

1. The 5^thpercentile of the weight of males 36 months of age is 12.0 kg.
2. The 95^thpercentile of the length of newborn females is 53.8 cm.

One variable that is measured by online homework systems is the amount of time a student spends on homework for each section of the text. The following is a summary of the number of minutes a student spends for each section of the text for the fall 2014 semester in a college statistics class at UHWO.

Q1 = 42         Q2 = 51.5         Q3 = 72.5

3. Provide an interpretation of these results.
4. Determine and interpret the interquartile range.
5. Suppose a student spends 2 hours doing homework for a section. Is this an outlier?
6. Do you believe that the distribution of time spend doing homework is skewed or symmetric? Explain your answer.

Question 5

A researcher is undertaking an early stage investigation into the possible effect of a food additive on the weight of rats. The additive is a “designer” chemical aimed at increasing growth rate. Data from the experiment are contained in the file STA201 201960 Assignment 2 Rat Diets.xlsx. (a) Show the data in a structure that allows it to be readily analysed using R Commander. (1 mark) (b) The researcher intends to determine if there is evidence that the additive has increased the weight of rats. State the appropriate null and alternate hypotheses in this instance. (c) Show the output when R Commander is used to undertake the relevant Welsch two sample t test, using a 5% level of significance. (d) Clearly state the conclusion for the test and justify this by referencing a value or values from the R Commander output. (e) State the statistical assumptions underlying Welch’s two sample t test. (f) Say if it would have been appropriate here to use the paired t test and justify your decision.

I have three errands to take care of in the Administration Building. Let  X_i = the time that it takes for the ith errand

(i = 1, 2, 3),and let X₄ = the total time in minutes that I spend walking to and from the building and between each errand. Suppose the

X_i's are independent, and normally distributed, with the following means and standard deviations:

μ₁ = 16,

σ₁ = 4,

μ₂ = 6,

σ₂ = 1,

μ₃ = 8,

σ₃ = 2,

μ₄ = 14,

σ₄ = 3.

I plan to leave my office at precisely 10:00 A.M. and wish to post a note on my door that reads, "I will return by t A.M." How long should I estimate my trip will take if I want the probability of the trip taking longer than my estimate to be 0.01? (Round your answer to two decimal places.)

From each description, identify or infer the target population, the sampling frame, the unit of analysis, and the type of sample. Discuss whether the sampling strategy will allow the researcher to form inferences about the target population based on the sample.

Problem: To study factors related to a diagnosis of depression in elderly individuals. Sample: A random selection of 150 of the 300 residents diagnosed with depression in one year while in a particular geriatric facility, and 340 randomly selected from the 850 residents in the same facility who were not diagnosed with depression during that year.

b. Problem: To obtain information on routes and types of transportation used by people traveling with the city. Sample: Council of Governments has computerized dataset of 110,000 trips made in one year; 10 percent of the trips are randomly selected for intensive analysis.

1.

For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.82 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs,at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least oneof the 3 systems will detect it? Your answer should be rounded to 5 decimal places.

2.

An engineering school reports that 58% of its students were male (M), 39% of its students were between the ages of 18 and 20 (A), and that 32% were both male and between the ages of 18 and 20.

What is the probability of choosing a random student who is a female or between the ages of 18 and 20? Assume P(F) = P(not M).

Your answer should be given to two decimal places.

R programming

Babies born in the US have birth weights that are approximately normally distributed with mean 3.339 kg and standard deviation 0.573 kg.

Using R, determine:

a) What fraction of babies are more than 1.5 standard deviations from the mean in either direction?

b) What fraction of babies are more than 1.5 kg from the mean in either direction?

c) If you took a random sample of 100 babies, what is the probability that their mean weight Y is greater than 3.5kg?

Please include the code used to obtain the answer

uppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. (a) Find the probability that a light bulb lasts less than one year. (Round your answer to four decimal places.) (b) Find the probability that a light bulb lasts between six and ten years. (Round your answer to four decimal places.) (c) Seventy percent of all light bulbs last at least how long? (Round your answer to two decimal places.) yr (d) A company decides to offer a warranty to give refunds to light bulbs whose lifetime is among the lowest three percent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place? (Round your answer up to the next month.) months (e) If a light bulb has lasted seven years, what is the probability that it fails within the eighth year. (Round your answer to four decimal places.)

Suppose we know that the average height of Americans is 176cm with standard deviation of 6cm; and that the average height of Australians is 181cm with standard deviation of 8cm. Suppose in a room there are two individuals, who happen to be from the same country. We cannot hear their accents (so cannot guess in that way whether they are Americans or Australians), but we know these individuals’ heights, which are 178cm and 180cm. Assume that heights are normally distributed. Obtain the likelihood functions, and suggest the likely country of origin of these individuals.

When evaluating a chi-square test, describe the importance of the goodness of fit test. Provide an example and explain how the test is used to evaluate the data.

Arsenic occurs naturally in very low concentrations. In healthy human adults arsenic blood concentrations are approximately Normally distributed with mean 3.9 μg/dL (micrograms per decilitre) and standard deviation 1.4 μg/dL. For the purposes of this question, assume that the distribution of arsenic blood concentrations is exactly as just described.

(a) What proportion of healthy adults have arsenic blood concentrations between 2 and 4.5 μg/dL?

b) Choosing a healthy adult at random, what is the chance that their arsenic blood concentration exceeds 6.8 μg/dL?

(c) What are the lower and upper limits of the middle 80% of arsenic blood concentrations in healthy human adults?

The following table presents the average price in dollars for a dozen eggs and a gallon of milk for each month in a recent year.

If a linear regression model were fit, what is the value of the slope and the value of the y-intercept? Please round to 3 decimal places as necessary. Treat the price of a gallon of milk as the response variable.