According to current enrollment records, 36% of students at the all-female Kovalevskaya College are pursuing undergraduate majors in STEM fields.Let the random variable,x, represent a student selected at random from among the 2500 undergraduates at Kovaleskaya College.

Before solving problems involving this context, explore the underlying probability distribution and its characteristics.Whatdiscrete probability distributionbest describes this context? Express the answers as requested without extra characters; with decimal answers, report the results rounded to four digits, as#.####

When considering this probabilistic context about female students at this fictitiouscollegebeing ornotbeingSTEM majors,does it resemble that famous opening line from Shakespeare's Hamlet soliloquy,"To be or not to be?"

1. Yes
2. No

In other words,is it reasonable to describe this probability context as having exactly two outcomes?

1. Yes
2. No

Given that this probability context results in exactly two outcomes,its name is which of the following?

1. monomial
2. binomial
3. trinomial
4. multinomial

Is it appropriate to saythatthis probabilistic contextcannotbe modeled in terms of a random variable,where the random variable is the number of female students at this fictitious college are STEM majors?

1. Yes
2. No

How should this random variable be described?

1. As a continuous random variable for this probability distribution,taking on a spectrum of variables as precise as available instrumentation
2. As a discrete random variable for this probability distribution, taking on only selected values such as counting numbers

Characteristics of this particular discrete probability distribution include which of the following?

a.the number of trials is finite or limited

b.the trials are independentof each other

c.there are only two outcomes,or can be regroupedinto only two outcomes

d.the probabilities of the two outcomes are consistent or equivalent from trial to trail

e.all of these characteristics

f.none of these characteristics

FALSEorTRUE: The two outcomes can reasonably be described as representingsuccess(i.e.,the desired outcome of interest)andfailure(i.e.,its complement or opposite).

1. True
2. False

In this problem context about the fictitious women's college,is it reasonable to consider asuccessas identifying or selecting a female student who is a STEM major?

1. Yes
2. No

In this problem context about the fictitious women's college, ifasuccessis identifying or selecting a female student who is a STEM major, then afailureis selecting a female student who isnota STEM major,no disrespect intended to othermajors.

1. Yes
2. No

As a reminder,since the probabilities of success and failure are complementary, they should sum up to what amount,expressed as a whole percentage with percent symbol?Alternatively,you could express the amount as 1.

Answer:

Probability distributions routinelyreference theentirecollection, all possible data under consideration, when summarizing and making predictions about the chance of events related to the context.Therefore, is it appropriate to consider the collection as a sample ratherthan a population?

1. Yes
2. No

Parametric values for such random variables for a probability distributioncan be determined,for example, arguably by common sense for this particular distribution's expected value.These population parameters include themean,thestandard deviation, and thevariance.Sound reasonable?

1. Yes
2. No

Is the population mean,mu or, equivalent to the idea of expectation?In other words,wouldn't themeanfor a random variable for this probability distribution be the most likely or expected value?

Yes

No

Here's an example to consider, separate from the main context here,about determining expected value.

In an environmentally conscious community that hasn't yet imposed restrictions on paper and plastic bags in retailestablishments,40%ofpatrons provide their own reusable bags when shopping.In a random sample of size 40 at a randomly selected store,how many patrons would be expected to provide their own reusable bags?Express the answer as awhole number without units/labels or insignificant digits.Rounding shouldn't be necessary.

Answer:

FALSEorTRUE:The population mean for a discrete binomial probability distribution's random variable can be computed as follows:, wherenis the population or sample size under considerationandpis the probability of success.This affirms the common sense or intuitive approach to calculating expected value:multiply the collection size times the probability of the desired outcome.

1. True
2. False

Returning to the problem context about the fictitious women's college where 36%ofthe 2500 students are STEM majors, record your response to item #1 here.

#1:What is the expected number (i.e.,population mean) number of STEM majors anticipated from a population of this size?

Answer:

FALSEorTRUE:The population standard deviationfor a discrete binomial probability distribution's random variable can be computed as follows:, wherenis the population or sample size under consideration,pis the probability of success, andqor1-pis the probability of failureor the complement of the probability of success.The populationvariance is simply the standard deviation withoutsquare rooting:.

1. True
2. False

Record your response to item #2 here.

#2:What is the population standard deviation?

Answer:

Record your response to item #3 here.

#2:What is the population variance?

Answer:

Software spreadsheet functions can facilitate calculations, though note that older versions and different platforms might functions that are defined slightly differently; ALWAYS follow the promptsor check the HELP options.

=BINOM.DIST( ...

After inputting the number of successes, the total number of trials (or collection size), and the probability of success, all with comma separators, the last routine prompt is a logical argument.For a discreteprobabilitydistribution,does the response TRUE indicate cumulative probability, up to and including the number of successes, and FALSE indicate an exact probability for exactly the requested number of successes?

1. Yes
2. No

Record your response to item #4 here.

#4:When a random sample of25such undergraduates are selected, what is the likelihood thatexactly nine(9)are majoring in STEM fields?

Answer:

Record your response to item #5 here.

#5:When a random sample of25such undergraduates are selected, what is the likelihood thatexactly fourteen(14)are majoring in STEM fields?

Answer:

Record your response to item #6 here.

#6:When a random sample of25such undergraduates are selected, what is the chance thatat least six(6)but no more than eight(8) are majoring in STEM fields?

Answer:

Record your response to item #7 here.

#7:When a random sample of25such undergraduates are selected, what is the chance thatat least ten(10)but no more than twelve(12) are majoring in STEM fields?

Answer:

Record your response to item #8 here.

#8:When a random sample of25such undergraduates are selected, what is the chance thateither fifteen(15)or sixteen(16) are majoring in STEM fields?

Answer:

Record your response to item #9 here.

#9:When a random sample of25such undergraduates are selected, what is the probability thatat most five(5) are majoring in STEM fields?

Answer:

Record your response to item #10 here.

#10:When a random sample of25such undergraduates are selected, what is the probabilityat least thirteen(13) are majoring in STEM fields?

Answer:

Record your response to item #11 here.

#10:When a random sample of25such undergraduates are selected, what is the chance thatat more than seven(7)but less than nineteen(19) are majoring in STEM fields?

Answer:

As a bonus, make this pop culture connection.What is the title of the Katy Perry song whose chorus is all about this probability distribution?COMMENTS & HINTS:Report a three part answer, with eight letters total.The middle reply,B, is just a single capital letter; start the first and third words,A &C, with capitals.Ignore any punctuation that sometimes accompanies this title.

Answer:___________ _____________ ______________