Question

survey data were gathered on the unlv campus collecting information on the students academic standing and their favorite place in nevada to go for a hike. the raw data were as follows: ( a_{11}=81 ), ( a_{12}=91 ), ( a_{13}=34 ), ( a_{21}=77 ), ( a_{22}=79 ), ( a_{23}=49 ), ( a_{31}=59 ), ( a_{32}=81 ), ( a_{33}=41 ), ( a_{41}=81 ), ( a_{42}=108 ), ( a_{43}=55 ) the above raw data were then used to create the following contingency table. note that you will need to calculate the grand total before answering the question that appears after the table. calculate the probability that a student is a junior and her/his favorite place to hike is mount charleston. (for answers up to four decimal places, enter the number in the box below without rounding it. for answers that have more than four decimal values, round your answer to four decimal places).

Explanation:

Step1: Calculate row totals

• Freshman total: \(81 + 91+34=206\)
• Sophomore total: \(77 + 79+49 = 205\)
• Junior total: \(59+81 + 41=181\)
• Senior total: \(81+108 + 55=244\)

Step2: Calculate column totals

• Red Rock total: \(81+77 + 59+81=298\)
• Valley of Fire total: \(91+79 + 81+108=359\)
• Mount Charleston total: \(34+49 + 41+55=179\)

Step3: Calculate grand total

Grand total \(=206+205 + 181+244=836\) (also \(298+359+179 = 836\))

Step4: Use the formula for probability

The number of juniors whose favorite place is Mount Charleston is \(a_{33}=41\). The formula for probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{41}{836}\)

Answer:

\(0.0490\)