Question

A factory produces a gear that has a label weight of 20.4 grams. Assume that the...

A factory produces a gear that has a label weight of 20.4 grams.

Assume that the distribution of the weights of these gears is N(21.37,0.16),N(21.37,0.16), that is, a normal distribution with meanμ=21.37μ=21.37and variance of σ2=0.16.σ2=0.16.

Let XX denote the weight of a single gear selected at random from the production line.

(a) Find P(X>22.07)P(X>22.07). [2 marks]

(b) Suppose that 15 gears are selected independently and weighed. Let YY be the number of these gears that weigh less than 20.857 grams. Find P(Y≤2)P(Y≤2). [3 marks]

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A candy maker produces mints that have a label weight of 20.8 grams. Assume the distribution...
A candy maker produces mints that have a label weight of 20.8 grams. Assume the distribution of the weight of these mints is N(21.37,0.16). (a) Suppose that 15 mints are randomly selected and weighted. Let Y be the number of meints that weigh less than 20.8 grams. Find P (Y ≤ 2). (b) Suppose that 3 mints are indepencently picked, what is the probability that their combined weight is more than 65 grams? (c) Suppose that 2 mints are indepencently...
Let X equal the weight (in grams) of a nail of the type that is used...
Let X equal the weight (in grams) of a nail of the type that is used for making decks. Assume the distribution of X is N(8.78, 0.42). Let ? be the mean of a random sample of weights of n = 16 nails. Sketch, on the same set of axes, the graphs of the probability density functions of X and of ?. Comment on these two distributions. Find P(8.58 < X < 8.98) and P(8.58 < ? < 8.98). Compare...
The mean birth weight of infants in the United States is μ = 3315 grams. Let...
The mean birth weight of infants in the United States is μ = 3315 grams. Let X be the birth weight (in grams) of a randomly selected infant in Jerusalem. Assume that the distribution of X is N(μ, σ2), where μ and σ2 are unknown. 25 new-born infants randomly selected in Jerusalem yielded a sample mean of 3515 grams and a standard deviation of s = 500 grams. Use the data to test the null hypothesis H0: μ = 3315...
Practice question 4 The factory manufactures lego parts. We assume that the weight X [grams] follows...
Practice question 4 The factory manufactures lego parts. We assume that the weight X [grams] follows the N (1.95, 0.052) distribution and the lego parts are packed in packages of 100 parts. What is the probability that the weight of one lego part randomly removed from the package is between 1.8 g and 2.1 g? Specify a 95% confidence interval for the weight of the package. What is the probability that the weight of at most one lego part in...
Let X equal the weight of the soap in a 6 lb. box, where the distribution...
Let X equal the weight of the soap in a 6 lb. box, where the distribution of X is N(6.05, 0.0004). (a) Find P(X < 6.0171). (b) If 9 boxes of soap are selected at random from the production line, find the probability that at most 2 boxes weigh less than 6.0171 lb. each.
Assume that the octane level of mid-grade gasoline has a normal distribution with a mean of...
Assume that the octane level of mid-grade gasoline has a normal distribution with a mean of 89.15 and a standard deviation of 0.16. We take many samples of this gasoline and measure their octane levels. Problem 1: What proportion of the samples will have octane levels higher than 89.50? Solution: Let XX denote the octane level, which is normal with μ=89.15μ=89.15 and σ=0.16σ=0.16. We need to find the probability that XX is greater than 89.5089.50. P(X>89.50)=P(X−μσ>89.50−89.150.16)=P(Z>2.19)P(X>89.50)=P(X−μσ>89.50−89.150.16)=P(Z>2.19) Many normal probability tables...
In a city, 51 % of the population favors the incumbent, Dawn Morgan, for mayor. A...
In a city, 51 % of the population favors the incumbent, Dawn Morgan, for mayor. A simple random sample of 450 is taken. Use the normal approximation along with the continuity correction factor to find the probability that at most 230 respondents favor Dawn Morgan for mayor. Let XX be the number of respondents out of 450 that favor Dawn Morgan for mayor. Describe the distribution of XX and its parameters: ~  Select an answer χ² F T N B  ( n=n=...
1. A particular fruit's weights are normally distributed, with a mean of 416 grams and a...
1. A particular fruit's weights are normally distributed, with a mean of 416 grams and a standard deviation of 11 grams. The heaviest 17% of fruits weigh more than how many grams? Give your answer to the nearest gram. 2. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 1.9 days. Let X be the recovery time for a randomly selected patient. Round all answers to...
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote...
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution...
Based on the number of voids, a ferrite slab is classied as either high, medium, or...
Based on the number of voids, a ferrite slab is classied as either high, medium, or low. Historically, 5% of the slabs are classied as high, 90% as medium, and 5% as low. A sample of 20 slabs is selected for testing. Let X; Y; and Z denote the number of slabs that are independently classied as high, medium, and low, respectively a. What is the joint probability distribution of X; Y; and Z and what are it's parameteres (n,p1...)?...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT