For the next three questions, if computing the probabilities manually, carry four decimal digits in your calculations. Compute t
he probability of three occurrences in three time periods (to 4 decimals). Compute the probability of five occurrences in two time periods (to 4 decimals). Compute the probability of seven occurrences in one time period (to 4 decimals)
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Answer:
<em>The speed of sound at 20°C is 343.42 m/s.</em>
<em>You have to wait 1.75 seconds to hear the sound of the bat hitting the ball</em>
Step-by-step explanation:
<u>Speed of Sound</u>
The speed of sound is not constant with temperature. Generally speaking, the greater the temperature, the greater the speed of sound.
The approximate speed of sound in dry air at temperatures T near 0°C is calculated from:
The air is at T=20°C, thus the speed of sound is:
The speed of sound at 20°C is 343.42 m/s.
To calculate the time to hear the sound after the batter hits the ball, we use the formula of constant speed motion:
Where d is the distance and t is the time. Solving for t:
Substituting the values v=343.42 m/s and d=600 m:
t = 1.75 s
You have to wait 1.75 seconds to hear the sound of the bat hitting the ball
Let denote the value on the
-th drawn ball. We want to find the expectation of
, which by linearity of expectation is
(which is true regardless of whether the are independent!)
At any point, the value on any drawn ball is uniformly distributed between the integers from 1 to 10, so that each value has a 1/10 probability of getting drawn, i.e.
and so
Then the expected value of the total is