Chapter 07, Section 7.4, Problem 041A machine at Katz Steel Corporation makes 4-inch-long nails. The probability distribution of the lengths of these nails is approximately normal with a mean oinspector takes a sample of 25 nails once a week and calculates the mean length of these nails. If the mean of this sample is either less than 3.95 inches or greater than 4.05 inches, the inspector concludes that the machineneeds an adjustment. What is the probability that based on a sample of 25 nails, the inspector will conclude that the machine needs an adjustment?4 inches and a standard deviation of 0.09 inch. The quality controlRound your answer to 4 decimal places.Probability =the tolerance is +/-5%

Solution: Let X be the length of the nails. From the given information, X follows normal…

Answered: Chapter 07, Section 7.4, Problem 041 A…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A professor knows that her statistics students' final exam scores have a mean of 79 and a standard deviation of 12.4. In his class, an "A" is any exam score of 90 or higher. This quarter she has 25 students in her class. What is the probability that 7 students or more will score an "A" on the final exam?
The average speeds of cars on a highway are distributed according to a normal distribution. Today, John is on his way to work. As he enters the highway, he notices a car speeding by at 150 km/hr. Ten seconds later, another car speeds by at 160 km/hr. John concludes that today, cars must be going faster for some reason. A few minutes later, John gets into a minor accident. Once again, he concludes that it was inevitable - he got into the accident because cars were driving faster today. Explain what fallacies - if any-are involved in both of John's claims. Is John justified in his conclusions?
Central Limit Theorem 2. According to the International Graduation Association, on average, high school girls in Canada spend $\$ 223.55$ on a prom dress with a standard deviation of $\$ 18.14$. If 76 high school girls are surveyed in Canada, what is the probability that the mean cost of their dresses is between $\$ 225.00$ and $\$ 228.00$ ? 3. It has been estimated that $23 \%$ of nurses are offered to work overtime on a regular basis. If we randomly selected 225 nurses, what is the probability that $25 \%$ or less of them will be offered overtime on a regular basis? SP.VS.717
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Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil change facility will perform 40 oil changes between 10 AM and 12PM. Treating this as a random sample, there would be a 10% chance of the mean oil change time being at or below what value.
Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?
Does it seem to you that people tend to be absent more on some days of the week than on others? Recently, a major biotechnology firm collected data with the hope of determining whether or not its employees were more likely to be absent on some weekdays than on others. The firm examined a random sample of 130 employee absences. The distribution of these 130 absences is shown in the table below. The observed frequency for each category (each weekday) is shown in the first row of numbers. The second row of numbers contains the frequencies expected for a sample of 130 employees if employee absences at the firm are equally likely on each of the five weekdays. The bottom row of numbers contains the following value for each of the categories.
Two gamblers bet $1 each on the successive tosses of a coin: i.e., at each coin toss, player 1 pays $1 to player 2 if the coin shows ‘Heads’, and player 2 pays $1 to player 1 if the coin shows ‘Tails’. What is the mean and the standard deviation of the total winnings (measured in $, winnings can be negative) of player 1 after 6 tosses?
The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?
Answer for sections A , B , C
e) Suppose that weekly household expenditures on petrol are normally distributed, with a mean of $120 and a standard deviation of $50. i. A family is randomly selected. Find the probability that this family spends more than $245 per week on petrol? A 2.5 B 0.0062 C 0.9938 D 0.0202 ii. The government wants to promote public transport and will award a prize to the families who spend the lowest amount on petrol. If the government only wants to give a prize to 10% of households, what is the most that a family is allowed to spend on petrol each week to obtain the prize? A $56 B $184 C $3.50 D $217.60 In a sample of 25 families, what is the probability that the average weekly expenditure on petrol will be less than $105? ii. A 0.0668 B 0.9332 C 0.3821 D 0.6179
Body temperature. Suppose the body temperature of healthy individuals is approximately normally distributed with a mean of 37.0°C and a standard deviation of 0.4°C. a. If 130 healthy individuals are randomly selected, what is the probability that the average temperature for these individuals is 36.80°C or lower? b. Would you consider an average temperature of 36.80°C as unlikely to occur if the true average temperature of healthy individuals is 37.0°C?

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