Search & Filtering
A school principal claims that grade 11 students have a mean grade of 86 with a standard deviation of 4 . Suppose that the distribution is approximately normal . What is the probability that a randomly selected grade will be greater than 82 but less than 90
A car dealership has both Electric and Internal Combustion Engine (ICE) vehicles available for sale. 30% of customers looking to purchase a new car are interested in Electric vehicles, while the rest want ICE vehicles. On a particular day, the dealership had 17 people coming in to purchase a new car.
a) What is the mean value and the standard deviation of the number of people who were interested in purchasing an Electric vehicle?
b) What is the probability that the number of people who are interested in an Electric vehicle is more than two standard deviations away from the mean value?
c) The dealership only has 9 Electric vehicles and 13 ICE vehicles in stock. If the 17 people are served on a first-come-first-serve basis, what is the probability that all of them will be able to purchase the type of vehicle they want?
A renowned steel company produces metal products with a mean weight of 118 kg and standard deviation of 30 kg. Suppose a sample of 50 products is randomly taken and its mean weight was found to be 120 kg.
a) State the appropriate hypotheses to test whether the mean of sample products differ from the given mean weight.
b) Describe Type I and Type II errors in this context, and comment on the severity of each type of error.
c) Test the hypotheses stated in part (a) at a 1% level of significance, and comment on your findings.
what is the probability that a market inspector will discover at most three violations of the public health code
Netflix is investing heavily in releasing their own productions under the “Netflix Originals” label. A call was sent out for scripts to be produced as Netflix Originals. The proposed runtimes of the scripts submitted were found to follow a normal distribution with mean 95 minutes and standard deviation 18 minutes. Netflix executives decided to keep the runtimes of their originals between 80 minutes and 125 minutes.
a) What is the probability that a randomly selected script has a runtime longer than 112 minutes?
b) Determine the 90th percentile value for the proposed runtimes of the scripts.
c) What is the probability that a randomly selected script will not satisfy the runtime requirements?
d) Records show that movies with runtimes in the top 13.45% of the accepted range have the most viewer retention, and make the most revenue. Therefore, what should the minimum runtime of a Netflix Original be if it is to maximise viewer retention?
Suppose that a salesperson succeeds in making a sale with three in every 4 potential customers contacted. a particular week 5 new potential customers are conducted.
What is the probability read the salesperson will succeed in making at least 4 sales?
What will be the total area under the normal curve?
Relationship between X and Y. To test this relationship, a research team decides to conduct a study using a sample of tertiary students.
x= 7,9,9,2,8,5,7,6,8,10
y= 7,6,6,3,9,7,6,7,6,9
a. Use the data supplied in a table to manually calculate the correlation coefficient (r). Show all your calculations. (14 Marks)
b. What does the ‘correlation coefficient’ that you calculated tell you about the direction and strength (magnitude) of the relationship between information and readiness? (3 Marks)
c. Calculate and interpret the coefficient of determination for this relationship. (3 marks)
In statistics, a sample means__________.
Select one:
a. a portion of the sample
b. a portion of the total observations from a sampled data
c. all items under investigation
d. a portion of the population
Statistic is a numeric quantity, which is calculated from________.
Select one:
a. observations
b. population
c. data
d. sample
