Statistical Real World Phenomena

In a normal distribution, approximately 95% of the data lies within _ standard deviation of the mean.

In a normal distribution approximately 95 % of the data lies within 2 _____________________ _______________ of the mean.

In a normal distribution approximately __% lies within 3 standard deviations of the mean.

A manager oversees 11 female employees and 9 male employees. They need to pick 3 of thees employees to go on a business trip, so the manager places all 20 names in a hat and chooses at random. Let X = the number of female employees chosen.

Is X a binomial variable? Why or why not?

Choose 1 answer:

• Each trial isn't being classified as a success or failure, so X is not a binomial variable.

• There is no fixed number of trials, so X is not a binomial variable.

• The trials are not independent, so X is not a binomial variable.

• The situation satisfies each of the conditions for a binomial variable, so X has a binomial distribution.

This is an example of a binomial distribution:

In a game involving a standard deck of 52 playing cards, an individual randomly draws t cards without replacement. Y = the number of aces drawn.

• True

• False

This is an example of a binomial distribution:

60% of a certain species of tomato live after transplanting fro pot to garden. Eli transplants 16 of these tomato plants. Assume that the plants live independently of each other. Let T = the number of tomato plants that live.

• True

• False

This is an example of a binomial distribution:

In a game of luck, a turn consists of a player continuing to roll a pair of six-sided dice until they roll a double (two of the same face-values). Let X = the number of rolls in one turn.

• True

• False

LeBron James is a very popular professional basketball player in the US. Each game, players can commit a maximum of 6 personal fouls. Let's define the random variable F as the number of personal fouls LeBron James committed in a randomly chosen game from the 2016-2017 season. Here's the partially completed probability distribution of F. 

Find the missing probability in the table. 

P(F = 6) = ?

The first digits of data entries in most real-world data sets are not uniformly distributed. The most common first digit is 1, followed by 2, and so on, with 9 being the least common first digit. This phenomenon is known as Benford's Law.The table above is the probability distribution for Benford's Law where the random variable D represents the first digit in a data entry.

Find the indicated probability P(D≥2)=

The American Community Survey is completed by the US Census Bureau to obtain information about households in the US. One variable of interest is how many people reside in each household (vacant households were recorded as having zero people). Based on data from 2014, here is the partially completed probability distribution of H, the number of people residing in a randomly selected US household:

Find the missing probability in the table.

P(H=0)