The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.04 flawsper square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.(a) What is the probability that there are no surface flaws in an auto's interior?(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?(c) If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?Round your answers to four decimal places (e.g. 98.7654).(a) The probability is i!(b) The probability is i!(c) The probability is i

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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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A manufacturer knows that their items have a normally distributed length, with a mean of 10.1 inches, and standard deviation of 1.5 inches.If 11 items are chosen at random, what is the probability that their mean length is less than 9.5 inches?
A manufacturer knows that their items have a normally distributed length, with a mean of 6 inches, and standard deviation of 0.6 inches. If 22 items are chosen at random, what is the probability that their mean length is less than 5.9 inches?
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 5 inches. What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? If a random sample of ten 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches?
2. Suppose a store has a filling machine that fills 12 ounce bottles of juice. It is known that the amount of juice poured by this filling machine follows a normal distribution with a mean of 12.18 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more than 12.23 ounces of juice.
According to results from the analysis of chocolate bars in Chapter 3, the mean number of insect fragments was 14.4 in 225 grams. Assume the number of fragments follows a Poisson distribution.(a) What is the mean number of grams of chocolate until a fragment is detected?(b) What is the probability that there are no fragments in a 28.35-gram(one-ounce) chocolate bar?(c) Suppose you consume seven one-ounce(28,35-gram) bars this week. What is the probability of noinsect fragments?
A manufacturer knows that their items have a normally distributed length, with a mean of 11.6 inches, and standard deviation of 2.1 inches.If 12 items are chosen at random, what is the probability that their mean length is less than 11.4 inches?
Suppose the heights of students in a class follows normal distribution. The mean is 66 inches and the standard deviation is 5 What is the probability that a randomly selected student height is above 69 inches? What is the probability that the height will fall in between 45-54 inches? Which of the following intermediate step is involved in finding probability that a randomly selected student height is more than 70 inches?
A study by the American Heart Association studied the distribution of birth weights for 1295 newborns (preterm babies excluded). They found that the birth weight of human babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 1.09 pounds. (a.) What is the probability that a randomly chosen baby weighs more than 9 pounds at birth? (b.) What is the probability that a randomly chosen baby weights between 6 and 8 pounds at birth? (c.) What is the 80th percentile for birth weight?
The height of American women is believed to follow a normal distribution with mean μ = 5.38 feet and standard deviation σ = 0.2083 feet. (b) A study randomly selects 30 American women. What is the probability that the mean height of women in this sample is greater than 5.5 feet? (c) Another study randomly selects 50 American women. Will there be a lower or higher probability that the mean height of the 50 women in this sample is greater than 5.5 feet, compared to the study in part (b)? Explain. (d) Instead, for which of the two studies from parts (b) and (c) there is a higher probability that the mean height of the women in the sample is between 5.33 and 5.43 feet? Explain.
A manufacturer knows that their items have a normally distributed length, with a mean of 6.1 inches, and standard deviation of 1 inches. If one item is chosen at random, what is the probability that it is less than 3.9 inches long?
The amountof cashew nuts per packet (?), sold by a company,can be modelled usinga normal random variable with a mean of 115.0 grams and a varianceof 4.0 grams. Determine the probability that the amount of cashew nuts, in a randomly selected packetsold by this company,is: (a)more than 113grams; (b)between 117.5grams and 120grams.
4. Suppose that 60% of college students own a smart phone manufactured by Apple. If a random sample of 200 college students is selected, use the normal distribution to approximate the probability that the number of students in the sample owning a smartphone made by Apple will be less than 105. Is it reasonable to use the normal approximation here?

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