x f(x) (3) 0 0.15 1 ? 2 0.3 3 ? 4 0.2 the mean of the above distribution is known to be 2.15 (i.e., E(x)=2.15). Determine f(1) and (3). Compute the variance and the standard deviation for the above probability distribution. (Round your standard deviation to hree decimal places.) ariance standard deviation
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- Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) H = 5.6; o = 1.4 P(7 < xs 9) =the standard deviation is equal to Independent Activity 1 Beth's Bread and Pastry Shop determines the number of cupcakes sold per day with its corresponding probabilities. Find the mean, variance, and standard deviation of the probability distribution below. If Beth, the owner of the shop is claiming that the average number of cupcakes sold in a day is 150 pieces, do you think it is a believable claim? Number of cupcakes sold per day (x) 90 120 135 150 160 175 Probability P(x) Practice Activity 2 0.15 0.10 0.20 0.20 0.20 0.15 Analyze the following pairs of data and identify which of the following will most likely yield to a higher variance and higher standard deviation. Put a check mark on the appropriate box. 1. Number of students from different grade levels. Number of boys in a family with three children. 2. Number of fish inside the aquarium from different households. Number of fish inside a can from the different local brands of sardines. Number of COVID-19 patients from different…Standard Deviation: A company's quarterly sales in millions of dollars are distributed as follows: Calculate the standard deviation of the company's quarterly sales. SALES (MILLIONS) PROBABILITY 2 0.3 3 0.4 5 0.3
- A bus comes by every 15 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 15 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. The mean of this distribution is _____ The standard deviation is _____ The probability that the person will wait more than 4 minutes is _____ Suppose that the person has already been waiting for 1.7 minutes. Find the probability that the person's total waiting time will be between 2.5 and 5.6 minutes _____ 7% of all customers wait at least how long for the train?_____ minutes.A jar contains 3 nickels and 2 dimes. You reach in and randomly select 2 coins. Let Xrepresent the value of the two coins in cents. Find [a] theexpected value of Xand [b] the standard deviation of X.Round answers to 2 decimals. [a] Expected Value: __________ [b] Standard Deviation: __________P(x) 0.1 6 0.2 9. 0.1 11 0.6 Find the mean and standard deviation of this probability distribution. Give your answer to at least 2 decimal places. Mean: Standard Deviation:
- Use the probability distribution to complete parts (a) and (b) below. The number of school-related extracurricular activities per student Activities 0 1 2 3 4 5 6 7 0.059 0.121 0.163 0.178 0.212 0.129 0.085 0.053 Probability The mean is (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.) The standard deviation is (Round to one decimal place as needed.) (b) Interpret the results. The mean is, so the average student is involved in typical number of activities per student (Round to one decimal place as needed.) 3 or 4 activities. no activities. at least 5 activities. The standard deviation is, so the ining: 00-55-29Seatwork No. 2 Complete the table below and find the mean, variance and standard deviation of the following probability distribution. P(X) X- P(X) x2 - P(X) 1 1 5 6. 5 11 1 5 16 5 21 1 MEAN: VARIANCE: STANDARD DEVIATION:Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 0 1 2 3 Probability 0.269 0.295 0.241 0.144 The variance is 1.5. (Round to one decimal place as needed.) (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is 1.4. (Round to one decimal place as needed.) The standard deviation is 1.2 (Round to one decimal place as needed.) (b) Interpret the results. 4 0.038 The mean is so the average batch of 1000 machine parts has the typical number of defects in a batch of 1000 (Round to one decimal place as needed.) 5 0.013 0 The standard deviation is SO
- Find the indicated probability using the standard normal distribution. P(z 1.94)(1 point) When parking a car in a downtown parking lot, drivers pay according to the number of hours or fraction thereof. The probability distribution of the number of hours cars are parked has been estimated as follows: X 1 6 7 3 4 P(X) 0.232 0.102 0.113 0.079 0.059 0.04 0.032 0.343 A. Mean = 4.594 B. Standard Deviation = %3D The cost of parking is 4.25 dollars per hour. Calculate the mean and standard deviation of the amount of revenue each car generates. A. Mean = 867 B. Standard Deviation = %3D 2.Mean (E(x)) = np St. dev=Given the number of trials and the probability of success, find the mean, standard deviation1.n =12, p = 0.22. n = 20, p = 0.5In addition, find the indicated probabilities3. n =11, p = 0.05, find P(3 failures)4. n = 6, p = 0. 35, find P(at least 3 successes)5. A basketball player has a 60% chance of making each free throw. What is the probability that the player makes exactly three out of six free throws?6. The manufacturing sector contributes 17% of Canadas gross domestic product. A customer orders 50 components from a factory that has a 99% quality production rate (99% of the products are defect-free). Find the probability that:a) none of the components in the order are defectiveb) there is at least one defective product in the order.c) There are at least two defective products in the order.d) Expected number of defective parts.7. Approximately 3% of the eggs in a store are cracked. If you buy two dozen eggs, what is the probability thata) none of your eggs…