Question

ex#28: mitchell is on his schools track team. he recorded his times in the 100 - yard dash at each track meet last year.
100 - yard dash time (sec.)
a) what is his slowest time?
b) what is his fastest time?
c) what percent of his time is faster than 24 seconds?
ex#29 angie babysits to earn extra spending money. she recorded how much money she earned each time she babysat for a year.
a) what is her median pay?
b) what is her highest pay?
c) what is her lowest pay?
d) what percent of the time does she earn less than $25?
pretest/practice for summative#3
unit 3/7/11 practice (data analysis and problem solving)
unit 4/8/12 advanced algebra (no quadratics since that was sum#2)
unit 5/9/13 geometry/trig stuff
unit 3/7/11 practice (data analysis and problem solving)
#1 probability:
number of contestants by score and day

	5 out of 5	4 out of 5	3 out of 5	2 out of 5	1 out of 5	0 out of 5	total
day 2	2	3	5	5	4	1	20
day 3	3	3	4	5	3	2	20
total	7	9	13	16	9	6	60

the same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. each contestant received 1 point for each correct answer. the number of contestants receiving a given score on each day is shown in the table above.
no contestant received the same score on two different days. if a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on day 2 or day 3, given that the contestant received a score of 5 on one of the three days?

Explanation:

Ex - 27 (Daily tip totals)

Step1: Identify median from box - and - whisker plot

The line inside the box represents the median. For the daily tip totals box - and - whisker plot, the median is at $150$.

Step2: Identify highest value

The end of the right - hand whisker represents the highest value. Here, the highest tip is $180$.

Step3: Calculate range

The range is the difference between the highest and lowest values. The lowest value is $120$ (start of the left - hand whisker) and the highest is $180$. So, range = $180 - 120=60$.

Ex - 28 (100 - yard dash times)

Step1: Identify slowest time

The end of the right - hand whisker represents the slowest time. So, the slowest time is $28$ seconds.

Step2: Identify fastest time

The end of the left - hand whisker represents the fastest time. So, the fastest time is $18$ seconds.

Step3: Calculate percentage faster than 24 seconds

The box - and - whisker plot shows that the third quartile ($Q_3$) is at $24$ seconds. $25\%$ of the data lies above $Q_3$. So, the percentage of times faster than 24 seconds is $25\%$.

Ex - 29 (Babysitting pay)

Step1: Identify median pay

The line inside the box of the box - and - whisker plot represents the median. The median pay is $30$.

Step2: Identify highest pay

The end of the right - hand whisker represents the highest pay. The highest pay is $60$.

Step3: Identify lowest pay

The end of the left - hand whisker represents the lowest pay. The lowest pay is $10$.

Step4: Calculate percentage earning less than $25$

The first quartile ($Q_1$) is at $20$ and the median ($Q_2$) is at $30$. The value $25$ is between $Q_1$ and $Q_2$. Since $25\%$ of the data lies below $Q_1$ and we assume a uniform distribution between $Q_1$ and $Q_2$, the percentage of times she earns less than $25$ is approximately $25\%+( \frac{25 - 20}{30 - 20})\times25\%=25\% + 12.5\%=37.5\%$.

Probability problem

Step1: Find number of contestants who got a 5 on one of the three days

The number of contestants who got a 5 on Day 1 is 2, on Day 2 is 2, and on Day 3 is 3. So, the total number of contestants who got a 5 on one of the three days is $2 + 2+3 = 7$.

Step2: Find number of contestants who got a 5 on Day 2 or Day 3

The number of contestants who got a 5 on Day 2 is 2 and on Day 3 is 3. So, the number of contestants who got a 5 on Day 2 or Day 3 is $2 + 3=5$.

Step3: Calculate conditional probability

The conditional probability formula is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of getting a 5 on Day 2 or Day 3 and $B$ is the event of getting a 5 on one of the three days, then the probability is $\frac{5}{7}$.

Answer:

Ex - 27:
a) $150$
b) $180$
c) $60$
Ex - 28:
a) $28$ seconds
b) $18$ seconds
c) $25\%$
Ex - 29:
a) $30$
b) $60$
c) $10$
d) $37.5\%$
Probability problem: $\frac{5}{7}$