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Q1. Simulate 100 random normal variables with mean 1.5 and standard deviation 2. Create a histogram which shows the data in the range between -4 and 10. with class intervals of length 0.5 Make sure that your name and current date are also included in the histogram title on this and all the other histograms you generate for this exercise.
Q2. Find out how many of your 100 variables are bigger than 0. and estimate the proba¬bility that a single normal variable with mean 1.5 and standard deviation 2 is above 0. Write this estimate by kind on your histogram. and show on your histogram which area is being used as your estimate. Also, compute and write the theoretical value for this probability using the table of the normal distribution.
Q3. Simulate 100 sample means, each made by taking the average of 20 normal variables with mean 1.5 and standard deviation 2. Make a histogram of these sample means in the range -4 to 10 with class intervals of length 0.5. As in the previous question. estimate the probability that a sample mean is bigger than 0, write this estimate by hand on your histogram, and show which area is being used as the estimate. Also. compute and write the theoretical value for this probability using the table of the normal distribution.
Q4. What do you notice about the two histograms and (therefore) about the two estimates of the probability of getting above 0?
use the following sample data to test whether the GPA are different at the 0.05 level of significance.
4 clothing manufacturer tests SRS of 5 specimens of each fabric. Determine the probability that mean breaking strength of 5 untreated specimens exceeds 50 pounds?
There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these.
Assume you randomly sample one mouse from the colony. The probability his age will be between 55 and 70 days is?
Ann and Jim, two employees in a fast-food restaurant, play the following game while waiting for customers to arrive: Jim pays Ann 2 cents if the next customer does not arrive within 1 minute; otherwise, Ann pays Jim 2 cents. Determine Jim's averag..
He continues this until he draws a number that is less than the comparison value, at which point he continues his interrogation. If he draws a 3 as the comparison value, what is the expected number of lashes you will receive for that question?
You are planning to test a vaccine for a virus that has no vaccine. Since the disease is usually not serious, you will expose 100 volunteers to the virus. After some time, you will record whether or not each volunteer has been infected.
A contingency table has 5 rows and 4 columns. How many degrees of freedom are there?
Please use synthetic division and the remainder theorem to find the indicated function values:
An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour.
Suppose that in a random sample of size n, there are x1, x2, and x3 number of genotypes s1,s2 and s3 respectively where x1+x2+x3=n. What sort of distribution is this?
What if the size for each sample were increased to 20? Would a sample mean of 115 or more be considered unusual? Why or why not? Why is the Central Limit Theorem used?
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