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2. While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.

  1. What is the probability that a randomly selected depth is less than 3.50 m? 
  2. What is the probability that a randomly selected depth is between 2.15 m and 5.50 m? 
  3. What is the expected value of the water depth? 
  4. What is the standard deviation of the water depth? 

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

  1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.15 ounces and a standard deviation of 0.15 ounce.
  1. What is the probability that a randomly selected apple will contain less than 1.90 ounces?
  2. What is the probability that a randomly selected apple will contain between 1.90 and 2.40 ounces? 
  3. What is the probability that a randomly selected apple will contain more than 2.40 ounces? 
  4. 77% of the apples will contain at least how many ounces of juice? 

 

1. In its standardized form, the normal distribution 

(a) has a mean of 0 and a standard deviation of 1.

(b) has a mean of 1 and a variance of 0.

(c) has an area equal to 0.5.

(d) cannot be used to approximate discrete probability distributions.

 

2. For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770.

The value of Z is

(a) 0.18

(b) 0.81

(c) 1.16

(d) 1.47

 

3. For some value of z, the probability that a standard normal variable is below z is 0.2090. The value of Z is 

(a) -0.81

(b) -0.31

(c) 0.31

(d) 1.96

 

4. For some positive value of X, the probability that a standard normal variable is between 0 and +2x is 0.1255.

The value of X is 

(a)  0.99

(b) 0.40

(c) 0.32

(d) 0.16

 

5. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 35. minutes and a standard deviation of minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

(a) 0.3551

(b) 0.3085

(c) 0.2674

(d) 0.1915 

Opeele Kyinkafa sells different used 2005 GM cars in excellent condition. The value or the retail price (Price) of a car is dependent on a variety of characteristics such as number of miles the car has been driven (Mileage), manufacturer of the car (Make) such as Buick, Cadillac, Chevrolet, Pontiac, SAAB, and Saturn. The car price is also influenced by the body type (Type) such as sedan, convertible, coupe, hatchback and wagon. It is also affected by number of cylinders (Cylinders) in the engine, the engine size (Liter), cruise control which is an indicator variable representing whether the car has cruise control (yes) or no otherwise and Sound indicator representing whether the car has upgraded speakers (yes) or no otherwise. All cars in this data set were less than one year old when priced and considered to be in excellent condition. Determine which major variables are dummies and are dynamic? Identify 3 potential unobserved heterogenous factors in this dataset. Display the full descriptive statistics of the data in R. Why do you think some variables are starred (*)? What is the median for “price”, standard deviation for “mileage”, skewness for “cylinder” and mean for “sound”? Test if “price” is normally distributed using histogram, kernel density plot and the shapiro wilk test. Create a red scatterplot matrix of price, mileage, cylinder, liter, make. From your graph, is the correlation between price & mileage positive or negative? What’s the pearson correlation coefficient between price & mileage and between “cylinder” & “liter” correct to 2 d.p Create a correlation matrix of the dataset by finding the apt R command for converting all string/dummy variables From the matrix, identify 2 potentially good predictors? Identify 3 pairs of variables that are mostly multicollinear. Which 2 pairs of variables are least correlated? Identify 3 pairs of variables most highly correlated with Cylinder Generate a simple regression plot of price on mileage with a re fitted line. Run the whole multiple regression model (label the equation as "regprice") & use it to answer the other questions. Specify the regression model for the whole data keeping the exact names of the variables. Write the estimated regression equation. In one sentence, which variables are significant and which are not? Justify Is the regression model justifiable? Explain Interpret the coefficient of Mileage, MakeCadillac, TypeSedan, Cylinder, & Cruiseyes. Compare the price of a car with 130,000 mileage, 6 cylinders, 3.8 liters, with cruise and sound, was manufactured by Pontiac with a convertible body type with that of the price of a car with four cylinders, 120,000 mileage, 3.8 liters, without cruise nor sound, was manufactured by Cadillac with a hatchback body type. Which factor(s) appears to be causing a comparative difference (if any)? Using only the VIF, which one of the pairs of variables selected to be multicollinear may be deleted? Justify?

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