need someone who is good in probability and statistics.
a.salm
probability.docx1) For , give a) P (x < 70), b) P (x > 65), and c) P (62 < x < 73). (1.5)
a) P (x < 70) =
b) P (x > 65) =
c) P (62 < x < 73) =
2) For , which Z values correspond to a) x=54, b) x =61.5, and c) x=69? (1.5)
a) Z =
b) Z =
c) Z =
3) For , give a) P (10 < X < 17) and b) P (8 < X < 20). (1)
a) P (10 < x < 17) =
b) P (8 < x< 20) =
4) The lifespan of a certain type of car battery is normally distributed with a mean of 1248 days and a standard deviation of 185 days. If the supplier guarantees them for 1080 days, what proportion of batteries will be replaced under the guarantee? If the supplier wants to replace no more than 10% of the batteries under the guarantee, for how many days will they extend their guarantee? (2.5)
5) For a likelihood of success p = 0.6, what is the likelihood of three or fewer successes out of five attempts? What is the likelihood of between three and six successes (both included) out of seven attempts? (1)
a) Three or fewer out of five:
b) Between three and six out of seven:
6) For a likelihood of success p = 0.3, what is the likelihood of four or more successes out of six attempts? What is the likelihood of two successes? (1)
a) Four or more:
b) Two:
7) Give the complete distribution for a binomial distribution, for six repetitions. (1)
8) What are the binomial coefficients in the complete distribution for 7 repetitions? (1)
9) Attendance at a cinema has been analyzed and shows that audiences consist of 60% men and 40% women. If a random sample of six people was selected from the audience during a performance, find the following probabilities: a) The sample consists of six women; b) There are more than three men in the sample; c) There are fewer than three women in the sample. (1.5)
a) Six women:
b) More than three men:
c) Fewer than three women:
10) A quality control system selects a sample of three items from a production line. If one or more is defective, a second sample is taken (also of size three), and if one or more of these are defective, the whole production line is stopped. Given that the probability of a defective item is 0.05%, what is the probability that the second sample is taken? What is the probability that the production line is stopped? (2)
11) What is the likelihood of 5 trains arriving in a train station in a timespan of ten minutes, when the average number of trains arriving over such an interval is 8? What is likelihood of 3 or fewer train arriving? (1)
a) 5 trains:
b) 3 or fewer:
12) If a two yard piece of carpet shows three weaving errors on average, what is the likelihood that there will be between 3 and 5 errors in a two yard stretch? More than 4 errors? (1)
a) Between 3 and 5:
b) More than 4:
13) For a Poisson distribution, calculate the distribution for λ = 3, for values up to x = 7. (1)
14) A factory estimates that 0.25% of its production of small components is defective. These are sold in packets of 200. Calculate the percentage of the packets containing one or more defectives. (1)
15) If you know that the average weight of the people in a population is 160 lbs, and the variance is 25, what is the probability that the average weight in a sample of 16 people is over 165 lbs? What is the probability that the average weight in a sample of 36 is over 162.5 lbs? What is the probability that he average weight will be between 158 and 161 lbs? (1.5)
a) >165lbs average (sample of 16):
b) >162.5lbs average (sample of 36):
c) P(158 < x < 161):
16) For the population in question 15), which is the lower bound for the interval that contains the highest 5% of values? (1)
17) If we know that 30% of students at DU own a bike, what is the likelihood that at least 33% in a random sample of 50 own a bike? What is the likelihood that at least 40% in a sample of 30 own a bike? (1)
a) 33% (sample of 50):
b) 40% (sample of 30):
18) What is an unbiased estimator? Also, give one example for one. (1)
19) When you estimate the confidence interval for the population mean, which cases do you have to distinguish, and how do they influence your approach? (1)
20) For the following data set: 1.05, 0.99, 1.12, 1.03, 1.03 calculate mean and standard deviation, assuming a) that the data set represents the whole population of interest; and b) that the data set is a sample drawn from a larger population. (2)
21) For the following sample, what is the 95% confidence interval for the population mean: 25.6, 19.8, 22.3, 24.1, 18.7, 21, 20.5, 19.8, 22.7, 23.2 (n=10)? What is the 90% confidence interval? (1.5)
22) For the following sample, what is the 95% confidence interval for the population mean, if the population variance is known to be 9: 25.6, 19.8, 22.3, 24.1, 18.7, 21, 20.5, 19.8, 22.7, 23.2, 21.8, 22(n=12)? What is the 99% confidence interval if the population variance is unknown? (2)
23) 33% of the students in a random sample of n = 69 own University of Denver merchandise. Determine the 90% confidence interval for the population proportion of DU merch owners among the student population. (1)
