Three classmates want to know when a tennis ball and a balloon will reach the same vertical height above the ground. David hits
a tennis ball with his racquet and Tyler releases a balloon at the same time that Samantha starts a timer. Let x represent the time, in seconds, since the timer starts. The following graph shows the vertical height of the tennis ball and balloon, in feet. Which of the statements best describes the solutions to the system of equations?
There is one possible solution, but it is not viable.
There are two possible solutions, and both solutions are viable.
There are two possible solutions, but only one of the solutions is viable.
There is one possible solution, and it is viable.
There is one possible solution, but it is not viable.
There are two possible solutions, and both solutions are viable.
There are two possible solutions, but only one of the solutions is viable.
There is one possible solution, and it is viable.
1 answer:
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Answer:
(1) P( < 26 inches) = 0.0436
(2) P(27.5 inches < < 28.5 inches) = 0.2812
Step-by-step explanation:
We are given that the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.
Firstly, Let = mean vertical leap for the 36 players
Assuming the data follows normal distribution; so the z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean vertical leap = 28 inches
= standard deviation = 7 inches
n = sample of NBA player = 36
(1) Probability that the mean vertical leap for the 36 players will be less than 26 inches is given by = P( < 26 inches)
P( < 26) = P(
<
) = P(Z < -1.71) = 1 - P(Z
1.71)
= 1 - 0.95637 = 0.0436
(2) <em>Now, here sample of NBA players is 26 so n = 26.</em>
Probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is given by = P(27.5 inches < < 28.5 inches) = P(
< 28.5 inches) - P(
27.5 inches)
P( < 28.5) = P(
<
) = P(Z < 0.36) = 0.64058 {using z table}
P(
27.5) = P(
) = P(Z
-0.36) = 1 - P(Z < 0.36)
= 1 - 0.64058 = 0.35942
Therefore, P(27.5 inches < < 28.5 inches) = 0.64058 - 0.35942 = 0.2812