6. Find the following probabilities using the normal approximation to the binomial distribution with parameters n = 100, p = 0.8: (a) P(73 ≤ X ≤ 87), (b) P(73
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6. Find the following probabilities using the normal approximation to the binomial distribution with parameters n = 100, p = 0.8: (a) P(73 ≤ X ≤ 87), (b) P(73 <X< 88), (c) P(X ≥ 81), (d) P(X < 77).
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- Tony's Pizza Company finds that 69% of the general population likes pepperoni pizza. I buy pizza for 46 of my intro stats students and it turns out that only 24 of these students like pepperoni pizza. Use the normal approximation to the binomial distribution to estimate the probability of randomly selecting 46 people with 24 or fewer of them liking pepperoni pizza. (a) Find the mean. (b) Find the standard deviation. (c) Find the z-score. (d) Find the probability.The manufacturer of "1 kg" jars of jam wants to fill the jars with a mean weight of 1.045 kg and a standard deviation of 0.063 kg. (a) If these standards are being met, what is the probability that 4 randomly selected jars will have a mean fill weight of less than 1 kg? Assume fill weights are normally distributed. As in (a), but calculate for (i) n = 10 and (ii) n = 25. (b) (c) The line is stopped and the equipment checked if the mean fill weight of 10 randomly selected jars is less than 1.00 kg or if it exceeds 1.075 kg. What is the probability the line will be stopped if specifications are being met? What is the probability the line will be stopped if the mean weight of 1.045 kg is maintained (d) but variability increases such that the population standard deviation is now 0.134 kg?If the random variable X is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(X ≥ .75) is: (a) 0.2266 (b) 0.4525 (c) 0.7734 (d) 0.7500 (e) None of the above
- Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)Assume the random variable x is normally distributed with mean µ = 88 and standard deviation o = 4. Find the indicated probability. P(78Let the random variable X denote the length of time (in seconds) required to complete a certain task. Suppose that the completion times are normally distributed with a mean of 216 seconds and a standard deviation of 50 seconds. (i) Find the probability that the time needed to complete the task is between 260 and 290 seconds. (ii) Find the value of k if P(X < k) = 0.025. (iii) A random sample of 25 similar tasks is selected. Find the probability that the mean completion time will be more than 200 seconds.Suppose a random sample of 25 students is selected from a community college where the scores on the final exam (out of 125 points) are normally distributed having mean equal to 112 and standard deviation equal to 4. Find the probability that the sample mean deviates from the population mean µ = 112 by no more than 3.Fifteen items or less: The number of customers in line at a supermarket express checkout counter is a random variable with the following probability distribution. X 0 1 2 3 4 5 P(x) 0.05 0.25 0.30 0.25 0.10 0.05 Send data to ExcelA random variable follows the continuous uniform distribution between 10 and 210. a. Calculate the following probabilities for the distribution. 1. P(75 sxs 85) 2. P(40The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630The average amount of money spent for lunch per person in the college cafeteria is $6.28 and the standard deviation is $2.92. Suppose that 8 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal placeswhere possible. What is the distribution of XX? XX~ N(,) What is the distribution of ¯xx¯? ¯xx¯~ N(,) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $4.74 and $5.38. For the group of 8 patrons, find the probability that the average lunch cost is between $4.74 and $5.38. For part d), is the assumption that the distribution is normal necessary? NoYes1*SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman