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(a) How many different positive three-digit whole numbers can be formed from the four digits 2, 6, 7, and 9 if any digit can be repeated?
(b) How many different positive whole numbers less than 1000 can be formed from 2, 6, 7, 9 if any digit can be repeated?
(c) How many numbers in part (b) are less than 680 (i.e. up to 679)?
(d) What is the probability that a positive whole number less than 1000, chosen at random from 2, 6, 7, 9 and allowing any digit to be repeated, will be less than 680?
The class registrations of 120 students are analyzed. It is found that: 30 of the students do not take any of Applied Mechanics, Chemistry, or Computers. 15 of them take only Applied Mechanics. 25 of them take Chemistry and Computers but not Applied Mechanics. 20 of them take Applied Mechanics and Computers but not Chemistry. 10 of them take all three of Applied Mechanics, Chemistry, and Computers. A total of 45 of them take Chemistry. 5 of them take only Chemistry.
a) How many of the students take Applied Mechanics and Chemistry but not Computers?
b) How many of the students take only Computers?
c) What is the total number of students taking Computers?
d) If a student is chosen at random from those who take neither Chemistry nor Computers, what is the probability that he or she does not take Applied Mechanics either?
e) If one of the students who take at least two of the three courses is chosen at random, what is the probability that he or she takes all three courses?
Suppose that two machines I and II in a factory operate independently of each other. Past
experience showed that during a given 8-hour time, machine I remains inoperative one
third of the time and machine II does so about one fourth of the time. What is the
probability that at least one of the machines will become inoperative during the given
period?
We have 3 blue and 5 Red balls lay in a box, three balls are chosen randomly out of the box find the probability distribution for number of blue balls without replacement.
13. During a laboratory experiment, the average number of radioactive particles passing
through a counter in 1 millisecond is 4. What is the probability that 6 particles enter the
counter in a given millisecond?
14. The probability that a student at a local high school fails the screening test for scoliosis
(curvature of the spine) is known to be 0.004. Of the next 1875 students at the school
who are screened for scoliosis, find the probability that
(a) fewer than 5 fail the test;
(b) 8, 9, or 10 fail the test.
15. A research scientist reports that mice will live an average of 40 months when their diets
are sharply restricted and then enriched with vitamins and proteins. Assuming that the
lifetimes of such mice are normally distributed with a standard deviation of 6.3 months,
find the probability that a given mouse will live
(a) more than 32 months;
(b) less than 28 months;
(c) between 37 and 49 months.
construct a sampling distribution of the sample means such that the average number of mg of cholesterol in a cup of a certain brand of ice cream is 660mg and the standard deviation is 35mg
Calculate the residual for x=3 when given
Hours,x and Scores, y (3,60),(7,92),(6,88),(5,81),(6,85),(4,74),(5,82),(7,94),(4,76),(5,84)
1)A normal distribution has u=80 o=10. What is the probability of random selecting the following scores?
a) x > 75
b) x < 85
c) between the mean and score of 90
d) between the mean and score of 50
e) 75 < x <85
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2)Determine the z-score values in each of the following scenarios.
a)what z-score value separates the top 8% of a normal distribution from the bottom 92%?
b)what z-score value separates the top 72% of a normal distribution from the bottom 28%?
c)what z-scores value represents the middle 90% of the values in a normal distribution?
Data from a representative sample were used to estimate that 32% of all computer users in a recent year had tried to get on a Wi-Fi network that was not their own in order to save money. You decide to conduct a survey to estimate this proportion for the current year. What is the required sample size if you want to estimate this proportion with a margin of error of 0.04? Calculate the required sample size first using 0.32 as a preliminary estimate of p.
A marketing manager of a Zambian Indigenous Company took a random sample of 2000 customers who bought a newly introduced product and found that 500 customers knew about the product. After a vigorous advertisement, another sample of 1,500 of customers indicated that 700 customers knew about the new product. Test at 5% level of significance if the advertisement increased the number of customers who know about the new product
