(iii) In this question, you may use the table of areas under the standard normal curve, which is supplied to you. A random variable X is normally distributed with a mean of 60 and a standard deviation of 12. Find: (a) P(54 s X s75) . (b) the value of k such that P(X 2k)=0-063
Q: z score co z sore co raw score e raw score
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A: normal distributionμ = 1490σ = 312
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- A blood pressure test was given to 450 women ages 20 to 36. It showed that their mean systolic blood pressure was 119.2 mm Hg, with a standard deviation of 12.1 mm Hg. (a) Determine the z-score, to the nearest hundredth, for a woman who had a systolic blood pressure reading of 112.2 mm Hg.______(b) The z-score for one woman was 2.11. What was her systolic blood pressure reading? (Round your answer to one decimal place.) _____mm Hg(b) Scores for a particular standardized test are normally distributed with a mean of 80 and a standard deviation of 14. Find the probability that a randomly chosen score is i. No greater than 70ii. At least 95 iii. Between 70 and 95 iv. A student was told that her percentile score on this exam is 72%. Approximately what is her raw score3y, 0sysys1, Suppose that the joint density function for Y, and Y, is given by f(y,,Y2)={ Otherwise. 0, Then the value of P(0 s Y, <0.5, 0.25 s Y,) is equal to
- A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1471 and the standard deviation was 318. The test scores of four students selected at random are 1910, 1210, 2210, and 1370. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1910 is (Round to two decimal places as needed.)The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution ? = 0.5 and ? = 0.289. (a) Let x be the sample mean waiting time for a random sample of 17 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) ?x = ?x = (b) Answer part (a) for a random sample of 45 individuals. (Round your answers to three decimal places.) ?x = ?x = (c) Draw a picture of the approximate sampling distribution of x when n = 45. A graph has a horizontal axis with values from approximately −3.5 to 3.5. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0 on the horizontal axis, then decreases and exits the graph on the…Withdrawal symptoms may occur when a person using a painkiller suddenly stops using it. For a special type of painkiller, withdrawal symptoms occur in 4% of the cases. Consider a random sample of 2400 people who have stopped using the painkiller. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p is the proportion of people in the sample who experience withdrawal symptoms. (b) Find the standard deviation of (c) Compute an approximation for P(p <0.05), which is the probability that fewer than 5% of those sampled experience withdrawal symptoms. Round your answer to four decimal places.
- A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1511 and the standard deviation was 312. The test scores of four students selected at random are 1910, 1280, 2240, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The z-score for 1910 is (Round to two decimal places as needed.) The z-score for 1280 is (Round to two decimal places as needed.) The Z-score for 2240 is (Round to two decimal places as needed.) The Z-score for 1420 is (Round to two decimal places as needed.) Which values, if any, are unusual? Select the correct choice below and, if necessary, fill in the answer box within your choice OA. The unusual value(s) is/are (Use a comma to separate answers as needed.) OB. None of the values are unusual.A standardized test is given to a sixth-grade class. Historically the mean score has been 151 with a standard deviation of 21. The superintendent believes that the standard deviation of performance may have recently decreased. She randomly sampled 23 students and found a mean of 161 with a standard deviation of 18.2898. Is there evidence that the standard deviation has decreased at the α=0.05 level? Step 1 of 5 : State of the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places. Step 3 of 5 : Determine the value of the test statistic. Round your answer to three decimal places. Step 4 of 5 : Make the decision. Step 5 of 5 : What is the conclusion?Reaction time is the amount of time it takes to respond to a stimulus, and for automobile drivers, it is an important factor in staying safe while on the road by avoiding rear-end collisions. Reaction times vary from driver to driver and tend to be longer than one might think. A recent study determined that the time for an in-traffic driver to react to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1.24 seconds and standard deviation of 0.45 seconds. If we let X denote reaction time for automobile drivers, use the appropriate Normal Distribution to determine each of the following. 1. What is the probability that a driver has a reaction time less than 0.6 seconds? 2. Approximately what proportion of drivers have a reaction time more than 2.5 seconds? 3. Within what limits, centered about the mean, would you expect driver reaction times to lie with 95% probability? What are the z-scores for these limits? 4. What is the reaction time…
- Deandre is in his first semester at a certain university and is taking a calculus course with a large enrollment. He just took the first midterm exam and is nervous about his score. Among all of the students in the course, the mean of the exam was 67 with a standard deviation of 3. Deandre scored a 62 on this exam. (a) Find the z-score of Deandre's exam score relative to the exam scores among all the students in the course. Round your answer to two decimal places. z=0 (b) Fill in the blanks to interpret the z-score of Deandre's exam score. Make sure to express your answer in terms of a positive number of standard deviations. Deandre's exam score was standard deviations (Choose one) ▼ the mean exam score among all students in the course. Calendar ... 80 F3 F4 F6 F7 F8 F9 F10 F11 云The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution ? = 0.5 and ? = 0.289. (a) Let x be the sample mean waiting time for a random sample of 12 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) ?x = ?x = (b) Answer part (a) for a random sample of 40 individuals. (Round your answers to three decimal places.) ?x = ?x =
