A random variable represents the number of successes in 30 Bernoulli trials, each with probability of success p=0.6(A) Find the mean and standard deviation of the random variable.(B) Find the probability that the number of successes lies within 1 standard deviation of the mean.(A) The mean of the random variable is (Type an integer or a decimal.)The standard deviation of the random variable is approximately(Round to three decimal places as needed.)(B) P(# of successes lies within 1 standard deviation of the mean) ~(Round to three decimal places as needed.)

Given that, The random variable X is binomial. X~B(n=30,p=0.6) The binomial distribution is the…

Answered: A random variable represents the number…

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 probability of success on a single trial of a binomial experiment is known to be 0.9. The random variable x, number of successes, has a mean of 98. (a) Find the number of trials involved in this experiment. (Give your answer correct to the nearest whole number.) (b) Find the standard deviation of x. (Give your answer correct to two decimal places.)
The mean checkout time in the express lane of a large grocery store is 2.7 minutes, and the standard deviation is 0.6 minutes. The distribution of checkout times is non-normal (for one thing, it can be a lot longer than 2.7 minutes, but it can only be so short).(a) What is the probability that a randomly-selected customer will take less than 3 minutes? 0.69150.3085 It cannot be determined from the information given. (b) What is the probability that the average time of two randomly-selected customers will take less than 3 minutes? It cannot be determined from the information given.0.2389 0.7611 (c) The probability that the average time of 64 randomly-selected customers will take less than 2.8 minutes is (d) The probability that the average time of 81 randomly-selected customers will take less than 2.8 minutes is (e) The probability that the average time of 225 randomly-selected customers will take less than 2.8 minutes is (f) The probability that the average time of 400…
pls solve parts d and e
Suppose that a recent poll found that 48% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 350 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that t moral values is poor. The mean of X is. (Round to the nearest whole number as needed.) The standard deviation of X is (Round to the nearest tenth as needed.) (b) Interpret the mean. Choose the correct answer below. O A. For every 350 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. O B. For every 350 adults, the mean is the range that would be expected to believe that the overall state of moral values is poor. O C. For every 350 adults, the mean is the minimum number of them that would be expected to believe that the overall state of moral values is po O D. For every 168 adults, the mean is the maximum number of them that would be…
Let x be a random variable representing the starting salary of a first-year teacher in a city. A report claims that the mean starting salary of these first-year teachers is greater than $50,000. To test this claim we find that a random sample of 20 teachers has a mean starting salary of $51,425 with a sample standard deviation of $3,549. If you assume that the population mean is $50,000, find the P-value corresponding to the hypothesis that the mean starting salary of the first-year teachers is greater than $50,000.
Let x be a random variable representing the starting salary of a first-year teacher in a city. A report claims that the mean starting salary of these first-year teachers is less than $52,000. To test this claim we find that a random sample of 25 teachers has a mean starting salary of $51,875 with a sample standard deviation of $1,055. If you assume that the population mean is $52,000, find the P-value corresponding to the hypothesis that the mean starting salary of the first-year teachers is less than $52,000. A. 0.28 B. 0.56 C. 0.14 D. 0.36
In a study of life expectancy in a certain region, the mean age at death was 70 years, and the standard deviation was 5 years. The life expectancy (years) is assumed to follow a skewed distribution. Suppose that a random sample of 45 people from this region is selected. The mean life expectancy (years) of the sample is considered a random variable. What is its standard error? 0.5976 O 2.2361 O 5.2341 O 0.1111
A sample of size 86 will be drawn from a population with mean 90 and standard deviation 24. Use the TI-83 Plus/TI-84 Plus calculator. Part: 0 / 2 Part 1 of 2 (a) Find the probability that x will be between 89 and 91. Round the answer to at least four decimal places. The probability that x will be between 89 and 91 is X
Suppose that a recent poll found that 60% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 400 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. The mean of X is 240. (Round to the nearest whole number as needed.) The standard deviation of X is. (Round to the nearest tenth as needed.)
A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 5 inches. A random sample of 41 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)
How was 7.5 obtained?
The distribution of weekly salaries at a large company has a mean of $1000 and a standard deviation of $350. What is the probability that the mean of a random sample of weekly salaries of 50 employees will be at most $900? 0.0217 O 0.9783 O 0.3438 O Cannot be determined, because the distribution of the population is not normal.

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