Statistics and Probability Answers

 If the probability mass function of a random variable is given by 𝑃(𝑋 = 𝑟) = 𝑘𝑟 3 , 𝑟 = 1,2,3, 𝑓, 𝑓𝑖𝑛𝑑 (i)the value of k, (ii) 𝑃( 1 2 < 𝑋 < 5 2 /𝑋 > 1 3 ), (iii) the mean and variance of X.

A road is constructed so that the right-hand turn lane at an intersection has a capacity of three (3) cars. Suppose that 30% of cars approaching the intersection want to turn right. If a string of 15 cars approaches the intersection, what is the probability that the lane will be insufficiently large to hold all the cars waiting to turn right?

. Airplane engines operate independently in flight and fail with probability of 0.1. A plane makes a successful flight if at most half of its engines fail. Determine the probability of a successful flight for two-enginned and four-engined planes. 

A true-false test is given for five questions. To pass, you need at least four (4) questions to be correct. If you guess each answer, what is the probability that you’d pass the test? 

Suppose you are conducting a household survey in a village which has 100 houses. If you need a sample of 25 houses for your study, select the sample by: simple random sampling method and systematic sampling method

 There are 1000 students in the school of Engineering and Natural resources out of 20,000 in the whole Copperbelt university. In the study 200 were found to be smokers in the school and 1000 in the whole university. Is there a statistical significant difference between the proportions of smokers in the school and the university

The incidence of COVID 19-disease is such that on the average twenty percent people suffer from it. If 100 people are selected at random, what is the chance that not more than ten people suffer from COVID 19-disease

Does talking on mobile phones while driving distract people? Researchers measured the reaction times of 80 study participants as they talked on mobile phones and found that the average level of distraction from their driving was rated to be 60 percent. Explain what could be your population, Sample, sample statistic and characteristic. 

Shiraz is trying to flip her sneakers. She checks prices of 40 pairs of new in box limited edition Jordan's in the pink-teal colourway on several reseller sites and finds that they have a mean asking price of $213.00 with a standard deviation of $51.00. Develop a 99% confidence statement for the resale market of these shoes.

The margin of error for the 99% confidence interval is 

Answer for part 1

.

We can be 99% confident that the average asking price of pink-teal Jordan's is between $

Answer for part 2 and coordinate 1

 and $

Answer for part 2 and coordinate 2

.

The Alien Invasion Survival Test scores are normally distributed with a mean of 110 and a standard deviation of 31. READ QUESTIONS CAREFULLY.

David gets a score of 87. What percentage of people will score higher than him on the same test? 

Answer for part 1

%

Stephanie’s standard score (z) on the test is 2.3. What score did she get on the test? 

Answer for part 2

What percentage of test takers scored between 87 and 110 on the test? 

Answer for part 3

%