Historically, the SAT score of a randomly selected student has an unknown distribution with a mean of 1510 points and a standard deviation of 345.1 points. Let X be the SAT score of a randomly selected student and let X be the average SAT score of a random sample of size 44. 1. Describe the probability distribution of X and state its parameters μ and o: X~ unknown 1510, 345.1 ✓ and find the probability that the SAT score of a randomly selected student is between 1007 and 1670 points. 0.6060 x (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem the sample size is large (n>30) although the distribution of the original population is unknown to describe the probability distribution of X and state its parameters x and ox: (Round the answers to 1 decimal place) X~N (4x =| 1510 <, ox 52.0 and find the probability that the average SAT score of a sample of 44 randomly selected students is less than 1385 points. 0.0082 (Round the answer to 4 decimal places)

Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 124 The probability that a randomly selected adult has an IQ less than 124 is ​(Type an integer or decimal rounded to four decimal places as​ needed.)

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 less than -2.506°C.

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100μ=100 and a standard deviation sigma equals 20σ=20. Find the probability that a randomly selected adult has an IQ between 84 and 116.

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X = percent of fat calories. (a) Find the z-score corresponding to 40 percent of fat calories, rounded to 3 decimal places. (b) Find the probability that the percent of fat calories a person consumes is more than 40. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z- score. Use your z-score from part (a), rounded to one decimal place). Shade: Left of a value Click and drag the arrows to adjust the values. -3 -2 -1 2 3 4 -1.5 (d) Find the maximum number for the lower quarter of percent of fat calories. Round your answer to 3 decimal places.

Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviation of σ=12.5 beats per minute If 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

Assume that adults have IQ scores that are normally distributed with mean of mu = 100 and a standard deviation sigma=20, Find the probability that a randomly selected adult has an IQ 80 and 120 the probability that a randomly selected adult has an IQ between 80 and 120 is (type an integer or decimal rounfed to four decimal places as needed)

Assume that females have pulse rates that are normally distributed with a mean of mu equals 74.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. If 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 80 beats per minute.

Assume that adults have IQ scores that are normally distributed with a mean of mμ=100 and a standard deviation σ= 15. Find the probability that a randomly selected adult has an IQ less than 127. The probability that a randomly selected adult has an IQ less tha 127 is

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?