A notice is sent to all owners of a certain type of automobile, asking them to bring their cars to a dealerto check for the presence of a particular manufacturing defect. Suppose that only 0.05%of such cars havethe defect. Consider a random sample of 10,000 cars.a) What are the expected value and standard deviation of the number of cars in the sample that have theeffect?b) What is the (approximate) probability that more than 10 sampled cars have the defect?c) What is the (approximate) probability that no sampled cars have the defect?

Given: 0.05% of cars have a manufacturing defect. Sample size n=10,000 cars.

Answered: A notice is sent to all owners of a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Human pregnancies of healthy singleton fetuses (i.e., excluding pregnancies with early-term complications or miscarriages, and multiple births) are normally distributed with a mean of 266 days and a standard deviation of 13 days. What is the probability that a baby is born between 250 and 275 days? If we stipulate that a baby is premature when born at least 3 weeks early, what is the probability a randomly selected baby is premature? If we stipulate that a baby is overdue when born more than 2 weeks after the expected date, what is the probability a randomly selected baby is overdue?
An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state. The amount of juice obtained from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of .15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces?
3. Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.Find the 95th percentile for the mean time to complete one month's reviews.
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) Nature Kiss Granola comes in a medium-sized box. The weight of granola in the boxis normally distributed with a mean of 14 oz and a standard deviation of 0.4 oz.a) What is the probability that the amount of granola in a box selected at random isbetween 13.9 and 14.2 oz?b) What the probability that the mean amount of granola from a random sample of 9boxes is between 13.9 and 14.2 oz?c) Compare your answers for part a) and part b). Why is the probability in part b) muchhigher? Why would this be expected?
When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 20% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 67 of the dragon eggs to incubate. Consider all the possible samples of 67 dragon eggs. What is the mean number of yellow eggs in samples of 67 eggs? (that is the same as asking for the expected value of the number of yellow eggs) (Give answer correct to at least one decimal place.) mean = What is the standard deviation in the number of yellow eggs in samples of size 67? (Give answer correct to at least one decimal place.) standard deviation = What is the variance in the number of yellow eggs in samples of size 67? (Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.) variance =
A grocery store produce manager is told by a wholesaler that the apples in a large shipment have a mean weight of 8 ounces and standard deviation of 1.6 ounces. The manager is going to select 64 apples randomly. (a) The manager decides to return the shipment if the samples mean weight of 64 apples is less than 7.6 ounces. Assuming that the wholesaler’s claim is true, find the probability that the shipment of apples will be returned. (b) The manager is willing to risk a 1% chance of returning the shipment. Assuming the wholesaler’s claim is true and the sample mean weight of 64 apples falls below X bar ounces. Find X bar.
Suppose a box contains {0, 2, 3, 4, 6}. Suppose that 100 draws are made at random with replacement. The expected value for the sum is____. The standard deviation(SD) for the box is 2. Thus, the standard error(SE) for the sum of 100 draws is____.
When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 37% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 67 of the dragon eggs to incubate. Consider all the possible samples of 67 dragon eggs. What is the mean number of yellow eggs in samples of 67 eggs? (that is the same as asking for the expected value of the number of yellow eggs) (Give answer correct to at least one decimal place.) mean = What is the standard deviation in the number of yellow eggs in samples of size 67? (Give answer correct to at least one decimal place.) standard deviation = What is the variance in the number of yellow eggs in samples of size 67? (Remember to calculate the answer using at least 5 decimal places, then give answer correct to at least one decimal place.) variance =
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