A population of values has a normal distribution with = 51.9 and o= 65.5. If a random sample of size n = 10 is selected, a. Find the probability that a single randomly selected value is less than 109.9. Round your answer to four decimals. P(X< 109.9) = b. Find the probability that a sample of size n = 10 is randomly selected with a mean less than 109.9. Round your answer to four decimals. P(M < 109.9) =
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- On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 107 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual.b. Find the probability that a randomly selected person's IQ is over 94. Round your answer to 4 decimal places.c. A school offers special services for all children in the bottom 4% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.d. Find the 25th and 75th percentiles (a.k.a Q1 and Q3) Round your answers to 2 decimal places.Q1: Q3:The mean number of words per minute (wpm) typed by a speed typist is 133 with a variance off 144 What is the probability that the sample mean would differ from the population mean by greater than 2.9 wpm if 90 speed typist are randomly selected? Round answer 4 placesAssume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P61, the 61-percentile. This is the temperature reading separating the bottom 61% from the top 39%.P61 =
- The average American man consumes 9.7 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 1 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N Note: this shows 2 blank spots for answersOn a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 102 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual.Find the probability that a randomly selected person's IQ is over 99. Round your answer to 4 decimal places.A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.Q1: Q3: IQR:On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 117 and a standard deviation of 14. Suppose one individual is randomly chosen. Let X = IQ of an individual.b. Find the probability that a randomly selected person's IQ is over 108. Round your answer to 4 decimal places.c. A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places.Q1: Q3: IQR:
- The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,221. Let X = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. b. Find the probability that a randomly selected acre in the forest has fewer than 32,793 ants. c. Find the probability that a randomly selected acre has between 46,676 and 51,692 ants. d. Find the first quartile. ? ants (round your answer to a whole number) PLEASE ANSWER THE 3 SUBS B, C AND DLos Angeles workers have an average commute of 31 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.a. Find the probability that a randomly selected LA worker has a commute that is longer than 27 minutes. b. Find the 70th percentile for the commute time of LA workers. minutesAssume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P70, the 70-percentile. This is the temperature reading separating the bottom 70% from the top 30%.P70 = °C
- The average score of all golfers for a particular course has a mean of 74 and a standard deviation of 5. Suppose 100 golfers played the course today. Find the probability that the average score of the 100 golfers exceeded 75. Round to four decimal places. O A. 0.3707 B. 0.1293 O C. 0.0228 O D. 0.4772Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P87, the 87-percentile. This is the temperature reading separating the bottom 87% from the top 13%.P87 = °CPlease only answer b c d