Suppose that the heights of adult females is normally distibuted with population mean equal to 168cm and population standard deviation equal to 6cm. Let X denote the height of a randomly individual fro the population of adult females  d) What is the probabaility that X is in between 166cccm and 172cm? e) Suppose a smaple of 20 individuals are randomly selected from population of adult females. Let x̄ denote the mean height of this random sammple of adult females i) What is the distribution of x̄ in conventional statistical notation? ii)What is the probability that x̄ is in between 166.5 cm and 171.5cm

The heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. (show all work)a) If an individual woman is randomly selected, what is the probability that she has a height between 63 and 65 inches?b) If 100 women are randomly selected, find the probability that they have a mean height greater than 64 inches.c) If 75 women are randomly selected, find the probability that they have a mean height less than 62.1 inches

Assume that females have pulse rates that are normally distributed with a mean of μ=76.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete part a through c a) If 1 adult female is randomly selected. Find the probability that her pulse rate is less than 82 beats per minute  (Round to four decimal places as needed) b) If 4 adult females are randomly selected, find the probability that they have a pulse rates with a mean less than 82 beats per minute  (Round to four decimal places as needed) c) Why can the normal distribution be used in part (b) even though the sample size don't exceed 30?(options are the image below)

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of 36 and a standard deviation of 10. Suppose that one individual is chosen at random. Find the following (round to 4 decimal places) a) Find the probability that the percent of fat calories a person consumes is more than 40. b) Find the probability that the percent of fat calories a person consumes is less than 35. c) Find the maximum number for the lower quartile of percent of fat calories. d) The middle 70% of the percent of fat calories are from 4 to

Suppose the mean grade for a statistic midterm was 75 with Standard Deviation of 10.  Assume that the grades are normally distributed.   a) What percentage of students received a grade less than 70? b) If 2 students failed the exam i.e. their grades were less than 60, how many students took the test? ( Hint: Focus on x< 60 first)

The environmental protection agency rates the mean highway gas mileage of the 2013 Ford Edge to be 27 miles per gallon. Assume the standard deviation is 3 miles per gallon. Rental car company buys 60 of these car. a) commute the mean(ux) and the standard deviation (ox) of x. Round to 4 decimal places) b) what is the probability that the average mileage of the fleet is greater than 26.5 miles per gallon? (Make sure the normal curve with shaded area)  c) what is the probability that the average mileage of the fleet is between 26 and 26.8 miles per gallon? (Make sure to draw the normal curve with the shaded area)

A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine. a) Find the mean of the total volume of the beverage in the case. b) Find the standard deviation of the total volume of the beverage in the case. c) Find the mean of the average volume per bottle of the beverage in the case. d) Find the standard deviation of the volume per bottle of the beverage in the case. e) How many bottles must be included in a case for the standard deviation of the average volume per bottle to be 0.0025 ounces?

The standard deviation of pulse rates of adult males is more than 10 bpm. For a random sample of 130 adult​ males, the pulse rates have a standard deviation of 10.7 bpm.   Express the original claim in symbolic form.