Q8/ If the average height of 500 students in a secondary school is 151 cm, with a standard deviation of 15 cm, and assuming that the lengths are normally distributed, find the expected value of the students whose heights are between 120 and 155 cm. Note that 0.6064 = (0.27)p and 9808 .0 = (2,07)p 0.2587 D 0.7582 B 0.8572 0.5872 A A O B C O D O
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- Assume that the readings at freezing on a bundle 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 the probability of obtaining a reading greater than 2.042°C. P(Z > 2.042) =Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?The weight of a green forest frog has a normal distribution with mean 150.3 g and astandard deviation of 5g. Find the probability that a randomly selected frog weighs. Include formula and show working pleasei. Less than 153g ii. Between 150 g and 158 g
- Assume that females have pulse rates that are normally distributed with a mean of 76.0 beats per minute and a standard deviation of e- 12.5 beats per minute. Complete parts (e) through (c) below a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute The probability is 5048 (Round to four decimal places as needed.) b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute. The probability is (Round to four decimal places as needed.)The manager of a grocery store has selected a random sample of 100 customers. The average length of time these 100 customers to check out was 30 minutes. It is known that the mandand deviation of the checkest time is 1 minute With a 90 probability, the sample mean will provide a margin of error of 1645 10 196 1.96The average life of a brand of automobile tires is 30,000 miles, with a standard deviation of 2,000 miles. If a tire is selected and tested, find the probability that it will have a lifetime longer than 29,000 miles. Assume the variable is normally distributed. Round your answer to four decimal places (to the nearest ten-thousandth). Use the format such as 0.8234 to input your answer, not just “.8234” .
- Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 265 feet and a standard deviation of 40 feet. Let X be the distance in feet for a fly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels less than 264 feet. Round to 4 decimal places.Assume that the readings at freezing on a bundle 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 the probability of obtaining a reading between -0.338°C and 0.467°C. Use 4 decimal places.The average THC content of marijuana sold on the street is 10.4%. Suppose the THC content is normally distributed with a standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 10.3. c. Find the 75th percentile for this distribution. %
- Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 275 feet and a standard deviation of 35 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly hit fly ball travels less than 265 feet. Round to 4 decimal places.In a random sample of 7 cell phones, the mean full retail price was $537.40 and the standard deviation was $188.00. Further research suggests that the population mean is $429.39. Does the t-value for the original sample fall between - to 95 and to g5? Assume that the population of full retail prices for cell phones is normally distributed. The t-value of t = fall between - to 95 and to 95 because to 95 (Round to two decimal places as needed.)The average THC content of marijuana sold on the street is 10.9%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 10.8. c. Find the 79th percentile for this distribution. %