Suppose that the random variable X has mean u and variance o >0. What are the values of a and b>0 such that the random variable Y=a+bX has mean 0 and variance 1.
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- Noise pollution is measured in decibels. In California any motorcycle made after 1980 may not be any louder than 80 decibels. Harley Davidson claims their mean decibel rating on bikes is 70 with a variance of 10. The variance of the noise is questioned. Just because Harley has a mean that is less than 80, they could still be producing louder than acceptable bikes. The federal EPA conducts a sample of 30 bikes and determines the variance to be 20 decibels. Is there enough evidence to question Harley’s claim of 10 decibels?The nation of Olecarl, located in the South Pacific, has asked you to analyze international trade patterns. You first discover that each year it exports 10 units and im- ports 10 units of wonderful stuff. The price of exports is a random variable with a mean of 100 and a vari- ance of 100. The price of imports is a random variable with a mean of 90 and a variance of 400. In addition, you discover that the prices of imports and exports have a correlation of r = -0.40. The prices of both ex- ports and imports follow a normal probability density function. Define the balance of trade as the difference between the total revenue from exports and the total cost of imports. What are the mean and variance of the balance of trade? What is the probability that the balance oft trade is negative?Suppose that contamination particle size (in microm- eters) can be modeled as f(x)=2x³ for 1 < x. Determine the mean of X. What can you conclude about the variance of X?
- A normally distributed random variable has a mean of 449. If a score of 433 lies two standard deviations below the mean, find the variance of X.One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can you conclude about the pooled variance for these two samples?suppose that we have disjoint normal populations A and B and we want to find the standard error estimate for estimating the difference in their means. We have an IRS from A of size 8 with variance 25 and an IRS from B of size 9 with variance 16. What is the resulting standard error estimate if we assume both populations have the same population variance?
- Records from previous years for a casualty insurance company show that its clients average a combined total of 1.9 auto accidents per day, with a variance of 0.31. The actuaries of the company claim that the current variance, oʻ, of the number of accidents per day is not equal to 0.31. A random sample of 17 recent days had a mean of 2 accidents per day with a variance of 0.62. If we assume that the number of accidents per day is approximately normally distributed, is there sufficient evidence to conclude, at the 0.05 level of significance, that the actuaries are correct? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO O20 (c) Find the value of the test statistic. (Round…a sample of n = 10 score has ss= 108 what is the variance for this sampleIf Y is a random variable with a mean of 30 and a standard deviation of 10, what is the probability that Y is between 35 and 40?
- A certain IQ test is known to have a population mean of 100 and standard deviation of 15 in the general population. You want to test whether psychology majors have a different average IQ than the population as a whole. Assume the variance of IQ is the same for Psych majors as it is in the general population. Suppose that Psychology majors actually have an average IQ of 108. If you do a 2-tailed test at α= .05 with a sample of 56 Psychology majors, you will be able to reject the null hypothesis if the mean IQ of your sample is below [L] or above [H]. Find L and H values. Options listed below. [L] answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92. [H] Answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92.Suppose the horses in a large stable have a mean weight of 1354 lbs, and a variance of 9604. What is the probability that the mean weight of the sample of horses would be less than 1364 lbs if 43 horses are sampled at random from the stable?Suppose Y = 6x-8, where x is a random variable with mean 2 and a variance of 4/3. Determine the variance of the random variable y
