PAGE 6 EXAM I STAT 226 FALL 2017- FORMB Interim President Benjamin Allen decides
ID: 3048657 • Letter: P
Question
PAGE 6 EXAM I STAT 226 FALL 2017- FORMB Interim President Benjamin Allen decides to consult the Statistics Department in regards to this controversial issue. A professor in the department concludes that it may be best to look at the yearly cost of tuition for all Universities in the state of lowa. A the yearly cost of tuition for all Universities in lowa follows a normal distribution with mean $13,960 and standard deviation $3,250. Using this information, answer . Tuition Fighting increased attendance costs, lowa State learns they must increase student tuition. fter further research, it is discovered that Note 1: For full credit, for questions (A), (B), (C) and (D) of this problem, you must draw the normal curve and correctly label it corresponding to the situation described in the question Note 2: Use Table A and not the 68-95-99.7 (Empirical) rule to find the required probabilities. (A) What is the probability that a University in lowa charges less than S7,500 for yearly tuition? (Leave answer as a proportion, NOT a peroent, and report value to 4 decimal places.) Show work here, draw and label the normal curve: Std 32SO 7500 13980 3250 Final Answer: (B) What is the probability that a University in Towa charges more than $15,750 for yearly tuition? Leave answer as a proportion, NOT a percent, and report value to 4 decimal places.) Show work here, draw and label the normal curve: 5750 -139O 3250 outer is /390 : ·5507 , Final Answer: tto 1 er- - (C) What is the probability that a University in lowa charges less than S21,000 but more than $10,000 for yearly tuition? (Leave answer as a proportion, NOT a percent, and report value to 4 decimal places.) Show work here, draw and label the normal curve: 1000 10,00 top0o 21000 18042 -score Final Answer:Explanation / Answer
a) P(x < 7500)
= P((X - mean)/sd < (7500 - mean)/sd)
= P(Z < (7500 - 13960)/3250)
= P(Z < -1.99)
= 0.0233
b) P(X > 15750)
= P((X - mean)/sd > (15750 - mean)/sd)
= P(Z < (15750 - 13960)/3250)
= P(Z < 0.55)
= 0.7088
c) P(10000 < X < 21000)
= P((10000 - mean)/sd < (X - mean)/sd > (21000 - mean)/sd)
= P((10000 - 13960)/3250 < Z < (21000 - 13960)/3250)
= P(-1.22 < Z < 2.17)
= P(Z < 2.17) - P(Z < -1.22)
= 0.9850 - 0.1112 = 0.8738
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.