20. A population of values has a normal distribution with u = 232.7 and o = 65.3. You intend to draw a random sample of sizen = 175. Find the probability that a sample of size n = 175 is randomly selected with a mean less than 239.1. %3D
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- The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.3 minutes. 11 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. 1. Find the probability that the randomly selected 11 person team will have a total time more than 265.1? 2. The top 10% of all 11 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round?Suppose that the number of points scored in a game comes from a normal population with an average of 12 points and a standard deviation of 9 points. Estimate the chance that the average points scored in ten randomly selected games will exceed 14.2 points. A. 0.4034 B. 0.0073 C. 0.2198 D. 0.2297What is the probability
- 1a. A random variable Z is normally distributed with mean 0 and standard deviation 1. It is known that P(Z 2.4) = b. This is shown in the following diagram. a -1.6 2.4 Find P(-1.620. Jumbo shrimp are those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages u = 12.5 with a standard deviation of s = 1. and forms a normal distribution. What is the probability of randomly picking a sample of n average more than M = 13 shrimp per bag? 25 1-pound bags thatA population of values has a normal distribution with M=153.9 and O=82.9 You intend to draw a random sample of size n=115. A). Find P86, which is the score separating the bottom 86% scores from the top 14% scores. P86 (for single values) =__________ B). Find P86, which is the mean separating the bottom 86% means from the top 14% means. P86 (for sample means) =_________112.1 and o = 61.4. You intend to draw A population of values has a normal distribution with µ a random sample of size n = 212. a. Find P34, which is the score separating the bottom 34% scores from the top 66% scores.P34 (for single values) = b. Find P34, which is the mean separating the bottom 34% means from the top 66% means. P34 (for sample means) = Round to 1 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.11Please8.We are given a normally distributed random variable X with µ = 75 and σ = 5. Find P (X > 85). 2.Find k such as P(X<k) = 0.997. Interpret your result. 3.Find the two values where the middle 68.27% of the distribution of X lie.A population of values has a normal distribution with Lu = 148.6 and o = 47.9. If a random sample of size n = 24 is selected, a. Find the probability that a single randomly selected value is greater than 162.3. Round your answer to four decimals. P(X > 162.3) = b. Find the probability that a sample of sizen 162.3. Round your answer to four decimals. 24 is randonmly selected with a mean greater than P(M > 162.3) =