Homework Answers
For a normal distribution, the percentile score for the given percentile is calculated using the Z score which can be calculated using excel formula for given percentile value. The formula for the normal distribution is =NORM.S.INV(0.25), thus the Z score computed as -0.67.
Now using the Z score formula the percentile score is calculated as:
Thus 25th percentile score calculated as X = 7.99
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Suppose the diameter of a certain car component follows the normal distribution with X - Nu...
Question code 1A26 Suppose the diameter of a certain car component follows the normal distribution with...
Question code 1A26 Suppose the diameter of a certain car component follows the normal distribution with a mean of 18mm and a standard deviation of 4mm. If we randomly select one of these components, find the probability of the following a) that its diameter is between 9mm and 27mm b) that its diameter is greater than 10mm
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Suppose X1,X2, .. ,X, is a random sample from a standard normal distribution and let Z...
Suppose X1,X2, .. ,X, is a random sample from a standard normal distribution and let Z be another standard normal variable that is independent of X1, X2, .., X,. 9 9 9 Determine the distribution of each of the variables X, U and V. (a) (b) Determine the distribution of the variable 3Z NU Determine the distribution of the variable W- (c) (d) Determine the distribution of the variable R -4y (where Y is the variable from (C)
and let (b) Let X, X,...,X, be a random sample form the normal distribution Nu,o) Σ-...
and let (b) Let X, X,...,X, be a random sample form the normal distribution Nu,o) Σ- ΣΧ be the sample mean, S2 be the sample variance. j-1 n-1 Σ--Σ( - 1' -nΣΤ-β). (i) Prove that Using it, determine the distribution of X (ii) Find the m.g.f. of X. n ΣT- ) Σ- 7 7 n (iii) Indicate the distributions ofJ 2 , respectively. and (iii) Given that X and S are independent, derive the m.g.f of (n-15, and then, σ'...
3. Suppose that the length of iron rods from a certain factory follows the normal distribution...
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Suppose the variable x is represented by a standard normal distribution. What value of x is at the 60th percentile of the distribution? Equivalently, what is the value for which there is a probability of 0.60 that x will be less than that value? Please round your answer to the nearest hundredth.
4. If a process creates a part with a diameter that follows a normal distribution with...
4. If a process creates a part with a diameter that follows a normal distribution with a mean value of 106.7 mm and a standard deviation of 1.8 mm, in what range of diameters will 95% of the parts produced occur? Give your answer in the form of 106.7 x mm.
9] Suppose X is Normal random variable with mean 10 and SD 4. What is the...
9] Suppose X is Normal random variable with mean 10 and SD 4. What is the probability that X is between 7 and 13? [10] Suppose X is Normal random variable with unknown mean mu and SD 4. For what value of mu, 80th percentile of X will be 23? (11] Lifetime of Carbon 14, X, is modeled by Exponential distribution with mean of 8223.7 years Determine its half-life (50th percentile).
Question code 1A26 Suppose the diameter of a certain car component follows the normal distribution with a mean of 18mm and a standard deviation of 4mm. If we randomly select one of these components, find the probability of the following a) that its diameter is between 9mm and 27mm b) that its diameter is greater than 10mm
Problem 4. The lifetime of a certain battery follows a normal distribution with a mean of 276 and standard deviation of 20 minutes. (a) What proportion of the batteries have a lifetime more than 270 minutes? (b) Find the 90th percentile of the lifetime of these batteries. (c) We took a random sample of 100 batteries. What is the probability that the sample mean of lifetimes will be less than 270 minutes?
Suppose X1,X2, .. ,X, is a random sample from a standard normal distribution and let Z be another standard normal variable that is independent of X1, X2, .., X,. 9 9 9 Determine the distribution of each of the variables X, U and V. (a) (b) Determine the distribution of the variable 3Z NU Determine the distribution of the variable W- (c) (d) Determine the distribution of the variable R -4y (where Y is the variable from (C)
and let (b) Let X, X,...,X, be a random sample form the normal distribution Nu,o) Σ- ΣΧ be the sample mean, S2 be the sample variance. j-1 n-1 Σ--Σ( - 1' -nΣΤ-β). (i) Prove that Using it, determine the distribution of X (ii) Find the m.g.f. of X. n ΣT- ) Σ- 7 7 n (iii) Indicate the distributions ofJ 2 , respectively. and (iii) Given that X and S are independent, derive the m.g.f of (n-15, and then, σ'...
3. Suppose that the length of iron rods from a certain factory follows the normal distribution with known standard deviation o = 0.2 m but unknown mean u. Construct a 88% confidence interval for the population mean u if a random sample of n = 16 of these iron rods has sample mean of 6 m. Z= E = CI:
4. If a process creates a part with a diameter that follows a normal distribution with a mean value of 106.7 mm and a standard deviation of 1.8 mm, in what range of diameters will 95% of the parts produced occur? Give your answer in the form of 106.7 x mm.
9] Suppose X is Normal random variable with mean 10 and SD 4. What is the probability that X is between 7 and 13? [10] Suppose X is Normal random variable with unknown mean mu and SD 4. For what value of mu, 80th percentile of X will be 23? (11] Lifetime of Carbon 14, X, is modeled by Exponential distribution with mean of 8223.7 years Determine its half-life (50th percentile).
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