Statistics and Probability Answers

In a random sample of 100 units from an assembly line, 15 were defective. Does this constitute sufficient evidence at the 10% significance to conclude that the defective rate among all units exceeds 10%?

Consider a population consisting of 1,2,3,4 and 5. From the population, the mean of the sampling distribution of the sample means if n=2, n=3. and n=4

If X is normally distributed with mean 150.3cm and variance 25. Find the probability that X is more than 10cm difference from the mean

the best paper was wrongly scored 75 instead of 85 what will be the new mean if the average score of 24 students in a class in 58 marks

1. It is known from the records of the city schools that the standard test for mathematics test scores on problem solving is 5. A sample of 200 bright students was taken and it was found that the sample mean score is 75. Previous test showed out the population mean to be 70. Is it safe to conclude at 0.025 significance level that the sample is significantly different from the population?

1. A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample or 50 students were given the same test and showed an average score of 83.20. Is there evidence to show that this group has a lower performance than the ones in general at 0.05 significance level?

A roulette wheel is constructed in such a way that the numbers from 1 to 10 can fall into it and the probability of dropping a number (k + 1) is 2 times greater than dropping the number k (for k = 1; 2; 3; ... 9). Find the probability that: a falls the number 1; b to drop the number 10. Give the ending as a decimal number rounded to 3 digits after the decimal point.

A roulette wheel is constructed in such a way that the numbers can fall from 1 to 100 and the probability of a humerus falling (k + 1) is 2 times greater than a numerical drop (for k = 1; 2; 3 ; ... 9). Find the probability that: a falls the number 1; b to drop the number 10. Give the ending as a decimal number rounded to 3 digits after the decimal point.

Suppose (Ω, 𝒜, 𝑃) is a probability space and 𝐵 is an event with 𝑃(𝐵) > 0. Prove that (Ω, 𝒜, 𝑃(⋅ |𝐵)), where 𝑃(⋅ |𝐵) is the conditional probability given 𝐵, is a probability space.

If the number of flaws on a piece of plywood occurs randomly and follows the Poisson distribution with a mean of 1 per 5m^2

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(a) Find the probability that a piece of randomly chosen plywood will contain no flaws.

(b) The plywood is sold in pieces of size 3m^2. Find the probability that the plywood will contain no flaws.