Question

question 9 (multiple choice worth 6 points) mrs. goodman’s physics class built different - shaped parachutes to see which shapes were more effective. the students tested the parachutes by dropping them from a height of 20 feet and timing the fall. they calculated the summary below.

std dev	0.4 sec
min	2.3 secs
q1	3.1 secs
median	4.2 secs
q3	5.5 secs
max	6.4 secs

the students want to see what happens to their times when they drop the parachutes from 32 feet. they find that the time of every drop is increased by 2 seconds. find the new mean and standard deviation.

• mean, 6.6 seconds; standard deviation, 0.4 second
• mean, 2.6 seconds; standard deviation, 0.4 second
• mean, 6.6 seconds; standard deviation, 2.4 seconds
• mean, 4.6 seconds; standard deviation, 2.4 seconds

Explanation:

Step1: Analyze effect on mean

When a constant (2 seconds) is added to each data point, the mean also increases by that constant. Original mean is 4.6 secs. New mean = \( 4.6 + 2 = 6.6 \) secs.

Step2: Analyze effect on standard deviation

Standard deviation measures spread. Adding a constant to each data point doesn't change the spread, so standard deviation remains the same. Original std dev is 0.4 sec. New std dev = 0.4 sec.

Answer:

Mean: 6.6 seconds; standard deviation: 0.4 second (corresponding to the first option among the given choices)