For the 405 highway that car pass through a checkpoint, assume the speeds are normally distributed such that μ= 61 miles per hour and δ=4 miles per hour.

Calculate the Z value for the next car that passes through the checkpoint will be traveling slower than 65 miles per hour.

Calculate the Z value for the next car that passes through the checkpoint will be traveling more than 66 miles per hour.

Calculate the probability that the next car will be traveling more that 66 miles per hour is:

QUESTION 7. The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. (8 points)

2 Points each

a. What is the probability that a randomly selected tire will have a life of no more than 50,000 miles?

b. What is the probability that a randomly selected tire will have a life of at least 47,500 miles?

c. What percentage of tires will have a life of 34,000 to 46,000 miles?

d. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

Suppose gas costs $3 a gallon and the average car gets 28 miles per gallon. If Congress mandates that cars have to get 36 miles per gallon, by what percentage will this lower the costs of driving? If the elasticity of total miles driven (per year) with respect to the cost of driving is –1, by how much will total miles driven per year increase, assuming it is 10,000 miles at the beginning? How much will total annual gas consumption of the average car change as a result of the mandated program?

Suppose gas costs $3 a gallon and the average car gets 28 miles per gallon. If Congress mandates that cars have to get 36 miles per gallon, by what percentage will this lower the costs of driving? If the elasticity of total miles driven (per year) with respect to the cost of driving is –1, by how much will total miles driven per year increase, assuming it is 10,000 miles at the beginning? How much will total annual gas consumption of the average car change as a result of the mandated program?

A donor pledges $100,000 to the Shakespeare Foundation to be used only to support the summer Shakespeare Theater—an event that has been held every summer for 38 years. This is an example of a A. Conditional Contribution. B. Contributions with donor restrictions. C. Contributions with no donor restrictions. D. A decrease in net assets.

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% confidence interval for the population mean.

A random sample of 60 home theater systems has a mean price of ​$110.00. Assume the population standard deviation is ​$16.90.

The​ 90% confidence interval is what?

Think of a time when you had to locate someone in a crowd, such as a participant in a parade, a friend in a packed theater, or a runner in a marathon. Based on your experience, respond to the following:
Did you conduct a conjunctive search? If yes, how did the number of distracters and features affect your search?

Summary In this lab, you write a while loop that uses a sentinel value to control a loop in a C++ program that has been provided. You also write the statements that make up the body of the loop. The source code file already contains the necessary variable declarations and output statements. Each theater patron enters a value from 0 to 4 indicating the number of stars the patron awards to the Guide’s featured movie of the week. The program executes continuously until the theater manager enters a negative number to quit. At the end of the program, you should display the average star rating for the movie. Instructions Ensure the source code file named MovieGuide.cpp is open in your code editor. Write the while loop using a sentinel value to control the loop, and write the statements that make up the body of the loop. The output statements within the loop have already been written for you. Ensure you include the calculations to compute the average rating. Execute the program by clicking the Run button. Input the following: 0, 3, 4, 4, 1, 1, 2, -1 Ensure the average output is correct.

this is the prewritten code:

// MovieGuide.cpp - This program allows each theater patron to enter a value from 0 to 4

// indicating the number of stars that the patron awards to the Guide's featured movie of the

// week. The program executes continuously until the theater manager enters a negative number to

// quit. At the end of the program, the average star rating for the movie is displayed.  

#include <iostream>

#include <string>

using namespace std;

int main()

{

   // Declare and initialize variables.

   double numStars;            // star rating.

   double averageStars;    // average star rating.

   double totalStars = 0;    // total of star ratings.

   int numPatrons = 0;           // keep track of number of patrons

   // This is the work done in the housekeeping() function

   // Get input.

   cout << "Enter rating for featured movie: ";

   cin >> numStars;

   // This is the work done in the detailLoop() function

   // Write while loop here    

   // This is the work done in the endOfJob() function

   cout << "Average Star Value: " << averageStars << endl;

   return 0;

} // End of main()

The lifetimes (in miles) of a certain brand of automobile tires is a normally distributed random variable, X, with a mean lifetime of µ = 40000 miles and standard deviation σ = 2000 miles. The manufacturer would like to offer a guarantee for free replacement of any tire that does not last a specified minimum number of miles. If the manufacturer desires to have a replacement policy that they will need to honor for only 1% of all tires they sell, what number of miles should be included in the following guarantee: “We will replace any tire free of charge if the lifetime of the tire is less than -----------------------------miles.” (That is, what is the largest value for a lifetime a tire can have and still be among the shortest 1% of all tires’ lifetimes?) Round to the nearest mile.

Speeding on the I-5. Suppose the distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 73 miles/hour and a standard deviation of 4.65 miles/hour. Round all answers to four decimal places. What proportion of passenger vehicles travel slower than 72 miles/hour? What proportion of passenger vehicles travel between 66 and 73 miles/hour? How fast do the fastest 6% of passenger vehicles travel? miles/hour Suppose the speed limit on this stretch of the I-5 is 70 miles/hour. Approximately what proportion of the passenger vehicles travel above the speed limit on this stretch of the I-5?