A population distribution is normally distributed with =84 and =22. Use this information to determine the following two probabilities. Round solutions to four decimal places, if necessary. Find the probability that a single randomly selected observation is greater than 87. P(x>87)= Find the probability that a sample of 59 randomly selected observations has a mean greater than 87. P(x>87)=

The distribution of all registered nurses' salaries on the Treasure Coast is known to be normally distributed with a mean of $54,150 and a standard deviation of $500. Use this information to determine the following two probabilities. Round solutions to four decimal places, if necessary. Find the probability that a single randomly selected nurse's salary is greater than $53,992. P(x>53,992)= Find the probability that a random sample of 8989 nurses have a mean salary greater than $53,992. P(x>53,992)=

The distribution of all Indian River County grapefruit weights is known to be normally distributed with a mean of 318 grams and a standard deviation of 50 grams. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 6161 grapefruit has a mean weight greater than 300 grams. P(x>300)= Find the probability that a random sample of 6161 grapefruit has a mean weight between 296 and 329 grams. P(296

The distribution of the ages of of all IRSC students is known to be normally distributed with a mean of 22.0 years and a standard deviation of 6.2 years. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that a random sample of 3030 students has a mean age of less than 20.3 years. P(x<20.3)= Find the probability that a random sample of 3030 students has a mean age between 20.3 and 22.0 years. P(20.3

The mean weight of all Goliath grouper caught on the Treasure coast is 387 pounds, with a standard deviation of 73 pounds. Suppose a random sample of 90 Goliath Grouper from the Treasure Coast are caught and weighed. Determine the probability that the average weight of the sample of 90 Goliath Grouper is within 24 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to four decimal places, if necessary. P(x within 24 pounds of )=

According to the National Weather Service, the mean daily temperature in Port St. Lucie is 72.8 F, with a standard deviation of 6.8 F. Consider the mean daily temperature in Port St. Lucie for a sample of 31 randomly selected days. Determine the probability that the mean daily temperature of a sample of 31 randomly selected days is greater than the mean daily temperature by at least 2.0 F. Round the solution to four decimal places, if necessary. P(x greater than by at least 2F)=

The standard deviation of the lifespan of a certain brand of LED light bulbs is 24 months. The quality control department at this company takes a random sample of 60 LED light bulbs and finds the mean lifespan of sample is 163 months. What is the probability that this sample mean is within 1 months of the mean of all light bulbs produced by the company? Round the solution to four decimal places, if necessary. P(x within 1 months of )=

According to a recent Pew Research poll, 78% of Americans say that the U.S. economic system unfairly favors the powerful. In a recent sample of 910 Americans, 686 agreed that the U.S. economic system unfairly favors the powerful. Determine the values of p and p^. Round solutions to two decimal places, if necessary. p= p^=

There are a total of 18,420 IRSC students, 73% of which are under the age of 21. In a random sample of 863 students, 63% are found to be under the age of 21. Determine how many students in the population and the sample, respectively, are under the age of 21. Round solutions to the nearest whole number, if necessary. IRSC students are under the age of 21. students in the random sample of 863 IRSC students are under the age of 21.

Consider a population where 58% of observations possess a desired characteristic. Furthermore, consider the sampling distribution of a sample proportion with a sample size of n=214. Use this information to determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that in a random sample of 214 observations, greater than 62% of the observations possess the desired characteristic. P(p>0.62)= Find the probability that in a random sample of 214 observations, between 47% and 50% of the observations possess the desired characteristic. P(0.47

According to a recent Gallup Poll, 54% of Americans report that they are 'better off financially today than they were a year ago.' Let p^ be the proportion of people in a random sample of 150 Americans that say that they are better off financially today than they were a year ago. Determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that in a random sample of 150 Americans, greater than 46% say they are better off financially today than they were a year ago. P(p>0.46)= Find the probability that in a random sample of 150 Americans, between 55% and 60% say they are better off financially today than they were a year ago. P(0.55

According to the U.S. Census Bureau, 32.1% of Floridians have earned a bachelor's degree. Let p^ be the proportion of people that have earned a bachelor's degree in a random sample of 201 Floridians. Determine the following probabilities. Round solutions to four decimal places, if necessary. Find the probability that in a random sample of 201 Floridians, less than 20.8% have earned a bachelor's degree. P(p<0.208)= Find the probability that in a random sample of 201 Floridians, between 26.3% and 30.9% have earned a bachelor's degree. P(0.263

According to the New York State Board of Law Examiners, approximately 67% of people taking the New York Bar Exam passed the exam. Use this information to find the following probabilities. Round solutions to four decimal places, if necessary.

1. If 18 people who have taken the New York Bar Exam are randomly selected, what is the probability that at least 78% have passed? Round your answer to 4 decimal places. P(p0.78)=
2. If 46 people who have taken the New York Bar Exam are randomly selected, what is the probability that at least 78% have passed? Round your answer to 4 decimal places. P(p0.78)=
3. Why did the probability decrease?
   • The probability decreased since the sample size increased resulting in a narrower distribution which reduced the area of the right tail.
   • The probability decreased since the sample size decreased resulting in a wider distribution which increased the area of the right tail.

According to the Pew Research Center, 38% of Americans have not read a book in the past year. Let p^ be the proportion of people that have not read a book in the past year in a random sample of 873 Americans. Determine the following probabilities. Round probability solutions to four decimal places and p^ values to two decimal places, if necessary. Find the probability that in a random sample of 873 Americans, at least 340 people have not read a book in the past year. P(pP(p^)= Find the probability that in a random sample of 873 Americans, between 297 and 358 people have not read a book in the past year. P(