A COB student is randomly selected, find the following probabilities (please show your work and report your probabilities as a percent rounded to the nearest percent)

Class Standing | ||||||

Major | Freshman | Sophomore | Junior | Senior | Total | |

General Business | 50 | 20 | 23 | 23 | 116 | |

HCA | 5 | 7 | 15 | 21 | 48 | |

Management | 35 | 45 | 24 | 33 | 137 | |

Marketing | 20 | 16 | 14 | 24 | 74 | |

Accounting | 50 | 42 | 38 | 40 | 170 | |

Finance | 11 | 15 | 24 | 16 | 66 | |

Economics | 4 | 8 | 5 | 3 | 20 | |

The totals are from Fall 2019 enrollment as of 8/23/19 but the distribution by class standing are estimates. | ||||||

All majors are disjoint. |

a) The probability that this student is a sophomore: **answer****153/631 = .24247 or 24%**

b) The probability that this student is a junior and majoring in accounting.**Answer****38/631 =0.0602 or 6%**

c) P(Management U Senior): **Answer ****p(management) 137/631 = 0.2171, p(senior) 160/631 = 0.2536, p(senior and management) 33/631= 0.0523 p(management or senior) 0.2171 + 0.2536 â€“ 0.0523 = 0.4184**

d) If this student is a senior, what is the probability they are majoring in economics?**Answer****(3/631) / (160/631) = 0.0048 or 0.5% =0.0188**

e) Are class standing and major independent? Please support your answer mathematically.

f) Why did I make the caveat that all majors are disjoint? What does this mean?

g) You are interested in understanding the number of scholarships awarded to COB students. The scholarship office gives you the following information: Students can earn a maximum of 3 scholarships each year. 30% of COB students will earn 1 scholarship, 25% will earn 2 scholarships, and 20% will earn 3 scholarships. Treating number of scholarships as the random variable, construct a probability model for number of scholarships. Number of Scholarships (X) P(x=X)

h) Find the expected value and standard deviation for the number of scholarships.

i) Let us convert this into a binomial model where a success is defined as earing a scholarship and a failure is defined as not earning a scholarships. Using the information from part g, find p and q.

j) If the COB has 800 students, are the conditions met to use the normal model to approximate this binomial situation?

k) Using the normal model, what is the probability that at least 600 students earn a scholarship?

l) Using the normal model, find the IQR.

m) Using the normal model, what is the probability that no more than 620 students will earn a scholarship.