A study of social mobility in England looked at the social class reached by the sons of lower-class fathers. Social classes are numbered from 1 (low) to 5 (high). Take the random variable X to be the class of randomly chosen son of a father in Class 1. The study found that the distribution of X is Sons class 1 2 3 4 5 probability .48 .38 .08 .05 .01 A. What percent of the sons of lower-class fathers reach the highest class, Class 5?   B. Does the distribution satisfy the requirements for a discrete probability distribution?  C. What is P(X≤3)? D. What is P(X<3)? E. What is the probability a son of a lower-class father reaches one of the two highest classes?  F. What is the expected class that a son of a lower-class father would reach?

A certain group of women has a 0.29​% rate of​ red/green color blindness. If a woman is randomly​ selected, what is the probability that she does not have​ red/green color​ blindness?

11.2% of the population is 65 or older. Find the probability that the following number of persons selected at random from 25 people are 65 or older. The probability that at least 3 are 65 or older is?

A random sample of 88 U.S. 11th-12th graders was selected.  The two-way table summarizes the gender of the students and their response to the question “Do you have allergies?”  Suppose we choose a student from this group at random.  If the student has allergies, what is the probability that the student is female?

The table below shows the results of a survey that asked 1058 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at random.     Support   Oppose Unsure Total   Males 153 333 9 495 Females 230 303 30 563 Total 383 636 39 1058 Find the probability that the person is not unsure or is female.   ​P(is not unsure or is ​female)=

A tube of listerine tartar control toothpaste 4.2 ounces. As people use the toothpaste the amount remaining in any tube is random. Assume the amount of toothpaste remaining in the tube follows a uniform distribution. What is the probability that there is more than 1.5 ounces remaining in the tube?

The 2015 National Vital Statistics Report provides information on how the nearly four million live births that occurred in 2014 broke down by birth order. Choose at random a baby born in the United States in 2014. Baby's birth order Probability mean = 1 2 0.391 0.319 The few babies who were 9th or more in birth order are included in the "8" birth order group. In 2014, 39.1% of the nearly 4 million live births in the United States were to first-time mothers. 3 5 6 7 4 0.168 0.072 0.028 0.012 0.005 standard deviation = What are the properties of the sampling distribution of the proportion of births to first-time mothers in random samples of 500 births from 2014? (Enter your answer for the mean rounded to three decimal place and your answer for the standard deviation rounded to four decimal places.) 8 0.005

A researcher wanted to study the commuting habits of community college students and faculty. He wanted to compare their mode of transportation to the college. He asked if they walk, bike, or drive to campus. The following table represents the data that was collected.   Walks to campus Bikes to campus Drives to campus Total Students 70 22 78 170 Faculty 5 4 23 32 Total 75 26 101 202   A. Find the probability that a randomly selected member of faculty walks to campus.   B. If you are randomly selecting a person from those who bike to campus, what is the probability that you will select a student.   C. Perform a Test of Independence to determine if commuting habits are dependent on being a student or a faculty.

A certain group of women has a 0.06% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?