A standard quality check found that out of 200 light globes, 6 had a defect.(i) If the sample proportion is approximately normally distributed, show thatthe mean and sample standard deviation are 0.03 and 0.01206 respectively.Z0.40.50.60.70.8(ii) Find the z-score if 4 light globes in this sample are defective.(iii) Use the section of the table showing the values of P(Z

i) Suppose p is the true proportion of defected light globes.

Answered: A standard quality check found that out…

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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The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. (a) Find the z-score corresponding to 40 percent of fat calories, rounded to 3 decimal places. (b) Find the probability that the percent of fat calories a person consumes is more than 40. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z- score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value Click and drag the arrows to adjust the values. -3 -2 -1 2 3 4 -1.5 (d) Find the maximum number for the lower quarter of percent of fat calories. Round your answer to 3 decimal places.
An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
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The combined SAT scores for the students at a local high school are normally distributed with a mean of 1490 and a standard deviation of 298. The local college includes a minimum score of 2056 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement?P(X < 2056) =
A random sample of n=16 scores is obtained from a population with a standard deviation of 16. If the sample mean is greater than 8 points greater than the population mean, what is the z-score for the sample mean?
A large group of students took a test in Physics and the final grades have a mean of 70 and a standard deviation of 10. The passing score is 60. The distribution is approximately normal. Using the 68-95-99.7 (empirical) rule, find the percentage of the students(a) scored between 60 and 80.(b) scored between 50 and 90.(c) higher than 80. (d) should pass the test.
Assume that weights of adult females are normally distributed with a mean of 79 kg and a standard deviation of 20 kg. What percentage of individual adult females have weights between 73 kg and 85 kg? If samples of 64 adult females are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are between 73 kg and 85 kg? The percentage of individual adult females with weights between 73 kg and 85 kg is 23.6 % (Round to one decimal place as needed.) The percentage of samples of 64 adult females with mean weights between 73 kg and 85 kg is (Round to one decimal place as needed.)
Blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.5. Using chebyshev’s theorem what is the known percentage of women with platelet counts that are within 2 standard deviations of the mean?

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