A lot of 25 light bulbs consists of N₁ defectives and N₂ working bulbs. The buyer accepts thelot of N₁ + N₂ = 25 bulbs if the number of defectives, X among n = 5 items taken at randomand without replacement from the lot is less than or equal to 1. The operating characteristiccurve is defined as the probability of accepting the lot, namelyOC (p) = P(X ≤ 1) = P(X = 0) + P(X = 1),where p = N₁/25 is the probability of a bulb being defective.(a) Show that the probability of the picking exactly X defectives follows a hypergeometricdistribution.(b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p = 0.12 andp = 0.16.(c) Plot, using R, the operating characteristic curve for N₁ = 1 to N₁ = 4.

Answered: Image /qna-images/answer/cdf4a6a4-d238-4219-8b46-571c33bdb4dc.jpg

Answered: (a) Show that the probability of the…

A First Course in Probability (10th Edition)

10th Edition

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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Suppose the systolic blood pressure (in mm) of adult males has an approximately normal distribution with mean μ =125 and standard deviation σ =14. Create an empirical rule graph with the following: A title and label for the horizontal axis including units. Vertical lines for the mean and first 3 standard deviations in each direction with numerical labels on the horizontal axis Labels for the areas of the 8 regions separated by the vertical lines as well.
Suppose X is a non-standard normal variable, with a mean of 118, and std deviation of 15 (i.e. X~N(118,15)). You have an observation (z) on a standard normal scale (i.e. Z~N(0,1)). If z = -0.03, what is it on an X scale?
Q1.[5 points]: A researcher wants to assess if there is a difference in the average age of onset of a certain disease for men and women who get the disease. Let µ = average age of onset for women and µ2 = average age of onset for men. A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11.5 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4.5 years. Assume that ages at onset of this disease are normally distributed for each gender, and assume the population variances are equal. i. What are the appropriate null and alternative hypothesis? ii. What is the value of the test statistics? iii. Why you decided to use the test statistics in part ii ? For a significant level of 0.05, what is the critical value (or critical region)? What is the appropriate conclusion to this test? iv. V.
Suppose that a researcher is interested in estimating the mean systolic blood pressure, u, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate u. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 26 mm Hg, what is the minimum sample size needed for the researcher to be 99% confident that his estimate is within 4 mm Hg of u? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements). (If necessary, consult a list of formulas.)
The standard error of estimate is the standard deviation of the observed x-values about the predicted x values TRUE OR FALSE
B6. Pinan Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below. ANOVA table Source Regression Residual Total Regression output Variables Intercept Distance-X Answer the following questions. SS 1,864.5782 1,344.4934 3,209.07 Coefficients 12.3601 4.7956 df 1 28 29 MS 1,864.5782 48.0176 Std. Error 3.2915 0.7696 F 38.83 t(df=28) 3.755 6.231 a) Write out the regression equation. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage? b) How much damage would you estimate for a fire 5 miles from the nearest fire station?
The measurement of the distance to a certain object is accompanied by systematic and random errors. The systematic error equals 50 m. in the direction of decreasing distance. The random errors obey the normal distribution law with the mean-square deviation = 100 m. Find (1) the probability of measuring the distance with an error not exceeding 150 m. in absolute value, (2) the probability that the measured distance does not exceed the actual one.
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(a) Show that the probability of the picking exactly X defectives follows a hypergeometric distribution. (b) Determine the operating characteristic curve for p = 0.04, p = 0.08, p= 0.12 and p = 0.16. (c) Plot, using R, the operating characteristic curve for N₁ = 1 to №₁ = 4.