3. For the standardized normal distribution, the following probabilities is ? (1.26 < Z < 1.63) = %3D a) P(Z = 1.63) – P(Z = 1.26) b) P(Z = 1.63) + P(Z = 1.26) %3D %3D c) 0.5 – P(z= 1.63) d) b & c.
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- using 'standard Normal Table ' , calculate the following probabilities. 1. Pr(z < -1.12) 2. Pr(z >2.32) 3.pr(1.22 < z >2.53) 4.pr(-3.22 < z < 0.22) 5.pr(-2.36 < z < -0.50)The proportion of vehicles which drive above the speed limit on a freeway is 85%. Suppose 100 vehicles are randomly clocked. 20 If each speeding vehicle is issued a $185 speeding ticket, the expected value of the ticket amount is $________. a $15,725 b $14,560 c $13,480 d $12,485You may need to use the appropriate appendix table to answer this question. Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.) (a) The area to the left of z is 0.9750. 1.8 x (b) The area between O and z is 0.4750. (c) The area to the left of z is 0.7291. (d) The area to the right of z is 0.1271. (e) The area to the left of z is 0.8106. () The area to the right of z is 0.1894.
- The weekly salary paid to employees of a small company that supplies part-time laborers averages s800 with a standard deviation of $500. (a) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $300 per week. (b) If every employee receives a year-end bonus that adds $100 to the paycheck in the final week, how does this change the normal model for that week? (c) If every employee receives a 5% salary increase for the next year, how does the normal model change? (d) If the lowest salary is $300 and the meltian salary is $550, does a normal model appear appropriate?21 Los Angeles averages 266.5 sunny days per year. What is probability that Boston has at least as many sunny days as Los Angeles? a 0.0020 b 0.0031 c 0.0047 d 0.0073a) Grace Floral Shop sells several types of roses for all occasions. It is known that 43% of the roses that is sold by Grace Floral Shop are Eden Roses. 12 roses are ordered to put in a bouquet (i) Define the random variable for this situation and list its values (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii)State the conditions that influence your choice of distribution. (iv)Calculate the probability that at most 2 of the roses were Eden Roses. b) The number of telephone calls coming into Grace Floral Shop to place orders averages 3 per minute. (i) Define the random variable in this situation and list its values. (ii) Stating its parameter(s), what is the probability distribution of this variable? (iii)Compute the probability that 5 calls will arrive per minute. (iv)Compute the probability that 3 or more calls will arrive in a 3-minute interval?
- Required information An officer of the state lottery commission has sampled lottery ticket purchasers over a 1-week period at one location. The amounts distributed back to the purchasers and the associated probabilities for 5000 tickets are as follows: 2 5 Distribution, $ 0 Probability 10 0.013 0.045 0.025 NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 0.91 100 0.007 If tickets cost $2, determine the expected long-term income to the state per ticket, based on this sample. The expected long-term income to the state is 96 cents per ticket.The following table provides a probability distribution for the random variable x. Excel File: data05-15.xlsx f(x) 3 0.25 0.50 0.25 a. Compute E(x) , the expected value of x. b. Compute o 2, the variance of x (to 1 decimal). c. Compute o, the standard deviation of x (to 2 decimals).2. The annual commissions earned by sales representatives of Machine Products Inc., a manufacturer of light machinery, follow the normal probability distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5,000. a. What percent of the sales representatives earn more than $42,000 per year? b. What percent of the sales representatives earn between $32,000 and $42,000? c. What percent of the sales representatives earn between $32,000 and $35,000?
- The probability distribution for the number of automobiles sold during a day (x) at Bob Iron Motors isas follows. x f(x) 0 0.001 1 0.007 2 0.034 3 0.099 4 0.188 5 6 0.220 7 0.136 8 0.055 9 0.015 10 0.001 17 The probability that 5 automobiles will be sold is,a 0.232b 0.244c 0.257d 0.271Please no written by hand solution Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.6, 0.2, and 0.2, respectively, then what are the expected return and the standard deviation of the return on Kate❝s investment? Calculate the coefficient of variation for this investment. (Round expected return to 3 decimal places, e.g. 0.125 and round intermediate calculations and standard deviation to 5 decimal places, e.g. 0.07680.)The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?