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Check whether the set of vectors {1 + 𝑥, 𝑥 + 𝑥2
, 1 + 𝑥3
} is a linearly independent set of
vectors in P3
, the vector space of polynomials of degree ≤ 3
Random samples of size 3 are taken from a population of the numbers 3, 4, 5, 6 , 7 and 8. Construct the sampling distribution of the sample means and determine its standard deviation.
The weights of the Grade 11 students are known to be normally distributed with a mean of 54 kg and a standard deviation of 8 kg. Find the percentage of Grade 11 students with weights between 45 kg and 66 kg.
The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution, with a mean of 2.5 work-related injuries a month. What is the probability that in a given month, no work-related injuries occur? That at least one work-related injury occurs?
- Population consists of these three numbers 1 2 3 and 4 list all the possible samples of size n = 2 which can be drawn with replacement from the population.
According to one of the teachers in your school, the senior high school students sleep for 7 hours a day on a weekday. You wanted to prove this claim by making a survey of 50 senior high school students. You will be asking the students about how long they sleep in a regular weekday. Record the results of your survey. As a researcher, you need to compute the mean and standard deviation of your sample.
Create a 90%, 95%, and 99% confidence interval for the mean time of sleep for senior high school students. In your report, the raw data should be present, and the computation should be complete
derivative y = arctan4(3x5)
A machine produces cylindrical metal pieces. A sample of pieces is taken, and the diameter are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01 and 1.03 cm. Find the t-value for a 98% confidence interval for the diameters of the cylindrical metal pieces. Assume that the diameters are approximately normally distributed.
You are apart-time crew at a fast food chain.Suppose you serve a certain number of customers every hour.10,12,14 in 3 hours you have served.Assume that samples of size n=2 are randomly selected without replacement from the population.Find the population mean μ and the mean of the sampling distribution of the means
THE FOLLOWING ARE THE HEIGHTS OF FOUR STUDENTS IN CENTIMETERS. SUPPOSE SAMPLES SIZE 2 ARE TAKEN FROM THIS POPULATION OF FOUR STUDENTS.
STUDENTS HEIGHT (in cm)
CARDO 125
ALYANA 120
JOAQUIN 130
FLORA 110
a. how many samples are possible?
b. construct the sampling distribution of the sample means
c. construct the histogram of the sampling distribuyion of the sample means
