### MS 150 Statistics q09 • Name:

sound speed (m/s)
374.65
319.54
377.08
373.61
430.50
419.00
315.90
387.50
452.20

Students in SC 130 Physical Science measured the speed of sound by measuring the distance and duration of flight for a sound based on the time delay of the arrival of the echo. Teams recorded and calculated eleven different sound speeds seen in the table. The mean μ is 383 m/s. The standard deviation σ is 46 m/s. For the purposes of this quiz, presume that the distribution of data is normal about a point estimated population mean of μ of 383 m/s and a point estimated population standard deviation σ of 46 m/s.

1. __________ The speed of sound at 28° Celsius, the typical daytime temperature on Pohnpei, is 350 m/s. What is the z-score for 350 m/s?

For the following, use the following normal distribution functions.

=NORMDIST(x;μ;σ;1)
=NORMINV(p;μ;σ)

1. p(x ≥ 383) = __________ Based on the normal distribution, if more experiments were run, what percent of the experiments would produce a sound speed of 383 m/s or more?
2. p(x ≤ 350) = __________ Based on the normal distribution, if more experiments were run, what percent of the experiments would produce a sound speed of 350 m/s or less?
3. p(x ≥ 400) = __________ Based on the normal distribution, if more experiments were run, what percent of the experiments would produce a sound speed of 400 m/s or more?
4. p(350 ≤ x ≤ 400) = __________ Based on the normal distribution, if more experiments were run, what percent of the experiments would produce a sound speed between 350 m/s and 400 m/s?
5. p(x ≤ __________ ) = 0.20 Below what speed will occur the 20% slowest sound speeds?
6. p(x ≥ __________ ) = 0.20 Above what speed are found the 20% fastest sound speeds??