4. Let X1 and X2 be random samples from a standard normal distribution, answer the following questions a. What is the distribution of -? b. What is the distribution of (x, +X;)? :? z(*x-*x) .? X,+X, c. What is the distribution of- z(*x-'x)^ d. What is the distribution of if Z ?
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- If a distribution is normal with mean 11 and standard deviation 4, then the median is also 11. O True O False Cub it tion4/qui/attempt.phplattempt-8528868cmid-127283 ANSWER ALL QUESTIONS 1. (a) The Monthly expenditure of family is nomally distributed with mean riyals 100 and variance Riyals 64. Evaluate the probability that the expenditure of a family is @ between 110.5 and 125.75, (ii) at most 93.5. (b) P(Z < K) - 0.45. Evaluate K. II. Listed is data on profit and market capitalization for a sample of 5 different firms: Market 20 40 55 18 40 (X) Profit 30 35 22 18 (Y) A. Find the Karl Person's coeflicient of corelation B. Find an estimate of profit when market capitalization is 30 Anduom/mod/quir/attempt.php?attempt-852886&cmid 127283 C. Find an estimate of market capitalization when profit is 20 D. Estimate the simple linear regression model .00 01 02 03 04 .05 .06 07 .08 09 0120 0160 .0557 .0910.0948 1331 0239 0279 0675 0636 .1026 1064 0.0 0.1 O080 0199 .0319 .0359 .0753 .1141 .0000 .0040 .0398 .0438 0478 .0517 0596 .0714 0.2 .0793 0832 0871 0987 1103 0.3 1179 .1217 .1591 1950 .1255 .1293 1368 .1406…42. Let X have a Standard Normal Distribution. Find P(X > - 0.25). В. 0.59871 A. 0.49871 С. 0.69871 D. 0.79871
- Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. Let X = distance in feet for a fly ball. A) Give the distribution of X.X ~ ____ (_____ , _____) B) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 196 feet? (Round your answer to four decimal places.) C) Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.) P(X < k) =Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 8 days. O Part (a) In words, define the random variable X. O the mean time of all trials O the length, in days, of a criminal trial O the length, in hours, of a criminal trial O the number of trials that last 22 days O Part (b) Give the distribution of X. <-O(0-0) O Part (c) If one of the trials is randomly chosen, find the probability that it lasted more than 26 days. (Round your answer to four decimal places.) Sketch the graph. 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 Write the probability statement. O Part (d) 60% of all trials of this type are completed within how many days? (Round your answer to two decimal places.) days14. The life of Sunshine CD players is normally distributed with mean of 5.6 years and a standard deviation of 1.9 years. A CD player is guaranteed for three years. We are interested in the length of time a CD player lasts. (Enter exact numbers as integers, fractions, or decimals.)Give the distribution of X. X ~ [N/Exp/U/H/B] (____ , ____)
- The average wait time to get seated at a popular restaurant in the city on a Friday night is 12 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 14 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 12, 13, 11, 11, 14, 12, 13, 14, 14, 13, 13, 10, 13, 12 What can be concluded at the the � = 0.05 level of significance level of significance? For this study, we should use Correct The null and alternative hypotheses would be: �0: Correct Correct �1: Correct Correct The test statistic Correct = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is Correct � Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton mean is significantly more than 12 at � = 0.05, so there is…Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 43 minutes and standard deviation 23 minutes. A researcher observed 46 students who entered the library to study. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( , ) What is the distribution of ¯x ? ¯x ~ N( , ) What is the distribution of ∑x ? ∑x ~ N( , ) If one randomly selected student is timed, find the probability that this student's time will be between 45 and 48 minutes. For the 46 students, find the probability that their average time studying is between 45 and 48 minutes. Find the probability that the randomly selected 46 students will have a total study time less than 2116 minutes. The top 20% of the total study time for groups of 46 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? minutesSuppose that X is a normally distributed with mean 36 and standard deviation 18 find the given probability is, p(X>37)
- 9. (Back when campus what regularly open in the semester.) The length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 7.0 minutes and a standard deviation of 1.0 minutes. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.5 minutes. (A) 0.2674 (B) 0.3085 (C) 0.1915 (D) 0.3551Monthly cell phone bills for residents of a city have mean €60 and standard deviation €12.Simple random samples of 100 are drawn and the mean is determined for each sample. Usenormal distribution curves where necessary What is the probability that the mean of a sample is less than €65?What is the probability that the mean of a sample is between €55 and €75?Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?
