7.41 In a certain binomial distribution, 7 = 0.25 and n = 40. In using the normal approximation, a. What are the mean and standard deviation of the corresponding normal distribution? b. If x = the number of “successes" among the 40 observations, determine the following: P(x = 8), P(12 < x < 16), P(10 < x s 12), P(x ² 14). %3D %3D

J 1

6.2 The Standard Normal Distribution Table: Z-score and Probability In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.7 inches, and standard deviation of 5.1 inches. What is the probability that the height of a randomly chosen child is between 40.95 and 43.35 inches? Probability = (Use 4 decimal places.)

Assume that X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the following: a. P(Z < 13) b. P(Z > 9) c. P(6 < X < 14)

he mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. What is the median giraffe height?  ft.c. What is the Z-score for a giraffe that is 20 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 18.2 feet tall? e. What is the probability that a randomly selected giraffe will be between 18.9 and 19.6 feet tall? f. The 70th percentile for the height of giraffes is  ft.

Q1. Given a normal distribution with mean = 100 and standard deviation = 10. What is theprobability that a sample of 25 (n) has a mean (X) that is:a. less than 95?b. between 95 and 97.5?c. above 102.2?d. There is a 65% chance that X is above what value?

An IQ score has a Normal distribution with mean 50 and standard deviation 5. Assume we want a sample of size 9. What proportion of sample means (of size 9) are less than 46.1? (Select nearest answer if your exact answer is not provided below). Group of answer choices 0.16 0.05 0.01 0.0013

Assume 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. Let Z represent the reading of this thermometer at freezing. What reading separates the highest 46.73% from the rest? That is, if P(z > c) = 0.4673, find c. c = °C

Suppose that the weight of an newborn fawn is Uniformly distributed between 2.2 and 3.8 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. The mean of this distribution is  The standard deviation is  The probability that fawn will weigh exactly 2.4 kg is P(x = 2.4) =  The probability that a newborn fawn will be weigh between 2.9 and 3.7 is P(2.9 < x < 3.7) =  The probability that a newborn fawn will be weigh more than 2.72 is P(x > 2.72) =  P(x > 2.8 | x < 3.5) =  Find the 25th percentile.