Question

1. If the standard deviation of a sample is 0.15 liters/sec while the average reading was 25 liters/sec, what is the range that represents:68% of the data collected, 90% of the data collected, 95% of the data collected, and 99.7% of the data collected.
2. The distance an object traveled was 36±0.1 inches. At the same time, the time measured was 5±0.2 seconds. What are the average speed, the maximum uncertainty, the expected uncertainty, and the average peed with 95%confidence?

Answer 1

(there are more than 1 questions, as per policy i am answering first question)

the range that represents :

68% of the data collected

from the graph :

range : [mean - 1*SD, mean + 1*SD]

= [25-0.15, 25+0.15]

= [24.85, 25.15]

90% of the data collected

for 90% the z = 1.64

range : [mean - 1.64*SD, mean + 1.64*SD]

[25-1.64*0.15, 25+1.64*0.15]

= [24.754, 25.246]

95% of the data collected

for 95% the z = 1.96

range : [mean - 1.96*SD, mean + 1.96*SD]

[25-1.96*0.15, 25+1.96*0.15]

= [24.706, 25.294 ]

99.7% of the data collected.

from the graph :

range : [mean - 3*SD, mean + 3*SD]

= [25-3*0.15, 25+3*0.15]

= [24.55, 25.45]

(please upvote)