he number of ants per acre in the forest is normally distributed with mean 43,000 and standard deviation 12,168. Let X = number of ants in a randomly selected acre of the forest. 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 acre in the forest has fewer than 33,413 ants.

Use the formula to find the standard error of the distribution of differences in sample means, x⎯⎯1−x⎯⎯2x¯1-x¯2.Samples of size 100 from Population 1 with mean 95 and standard deviation 10 and samples of size 80 from Population 2 with mean 76 and standard deviation 17Round your answer for the standard error to two decimal places.standard error =

Today, the waves are crashing onto the beach every 5.6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.6 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 0.7 seconds after the person arrives is P(x = 0.7) = d. The probability that the wave will crash the beach between 1.6 and 5.1 seconds after the person arrives is P(1.6 3.72) = f. Suppose that the person has already been standing at the shoreline for 0.8 seconds without a wave crashing in. Find the probability that it will take between 1.4 and 3.3 seconds for the wave to crash onto the shoreline. g. 65% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the minimum for the upper quartile. seconds.

Today, the waves are crashing onto the beach every 4.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.1 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is C. The probability that wave will crash onto the beach exactly 2.8 seconds after the person arrives is P(x = 2.8) = d. The probability that the wave will crash onto the beach between 0.4 and 1.9 seconds after the person arrives is P(0.4 0.82) = f. Suppose that the person has already been standing at the shoreline for 0.5 seconds without a wave crashing in. Find the probability that it will take between 1 and 4 seconds for the wave to crash onto the shoreline. g. 26% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the maximum for the lower quartile. seconds.

Charlie will perform a hypothesis test at the a = 0.05 level. Felice will perform the same test at the a = 0.01 level.

Suppose that the weight of seedless watermelons is normally distributed with mean 6.2 kg. and standard deviation 1.5 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to two decimal places. A. X ~ N(  ,  ) B. What is the median seedless watermelon weight?  kg. C. What is the Z-score for a seedless watermelon weighing 8 kg?  D. What is the probability that a randomly selected watermelon will weigh more than 7 kg?  E. What is the probability that a randomly selected seedless watermelon will weigh between 4 and 5 kg?  F. The 80th percentile for the weight of seedless watermelons is  kg.

benk is 9.2 minutes with a standard deviation of The average waiting time for a drive in 2.6 minutes. Assume that the times A. Determine the probability, to 3 decimal places, t ustomer will have to wait less than 6 minutes. B. 20% of all customers will have to wait more than minutes. Round to 1 decimal place.

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. Round all answers to 4 decimal places if where possible a. What is the distribution of X? X N( b. Find the probability that a randomly selected fat calorie percent is more than 40. c. Find the minimum number for the lower quarter of percent of fat calories.

A student takes a true-false test that has 10 questions and guesses randomly at each answer. LetX be the number of questions answered correctly.  c)The mean and stand deviation of X (show work and round final answer to 2 decimal places) Mean: Standard deviation =