The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.2 years and a standard deviation of 0.5 years. He then randomly selects records on 28 laptops sold in the past and nds that the mean replacement time is 3 years. Assuming that the laptop replacement times have a mean of 3.2 years and a standard deviation of 0.5 years, nd the probability that 28 randomly selected laptops will have a mean replacement time of 3 years or less. P(M 5 3 years) =| Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact zscores or z- scores rounded to 3 decimal places are accepted. Based on the result above, does it appear that the computer store has been given laptops of lower than average quality? 0 Yes. The probability of this data is unlikely to have occurred by chance alone. 0 No. The probability of obtaining this data is high enough to have been a chance occurrence. A population of values has a normal distribution with ,u. : 154 and or : 14.5. You intend to draw a random sample of size n : 177. Find the probability that a single randomly selected value is greater thanx'l 57.4. P(X =- 1 57.4) = | | Find the probability that a sample of size n : 177 is randomly selected with a mean greater than 157.4. P(M > 157.4) = | | Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact zscores or zscores rounded to 3 decimal places are accepted. A population of values has a normal distribution with ,u : 54 and or : 39.6. You intend to draw a random sample of size n : 96. What is the mean of the distribution of sample means? re: i What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) JEZ| A particular fruit's weights are normally distributed, with a mean of 254 grams and a standard deviation of 24 grams. If you pick 10 fruits at random, then 3% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram. A manufacturer knows that their items have a lengths that are skewed right, with a mean of 11 inches, and standard deviation of 3.4 inches. If 35 items are chosen at random, what is the probability that their mean length is greater than 12.2 inches? (Round answer to four decimal places) x A population of values has a normal distribution with ,u. : 59.3 and or : 26.8. You intend to draw a random sample of size n : 20. Find the probability that a single randomly selected value is less than 53.3. Paxss$=| : "1. Find the probability that a sample of size n : 20 is randomly selected with a mean less than 53.3. HM