The integral part of performing arts is ‘Jumping’ that requires strong muscular strength and elasticity of dancers. At what height a dancer vertically jump is one of the measures of dancer’s leg power, and however, it also depends on the level of expertise and amount of training s/he received. A research study conducted among Malaysian undergraduate student martial arts athletes (29 male and 25 female) reports that male arts athletes jump twenty-six percentage higher than their female counterparts. Assume that 90% of male athletes exceed the jump height of female counterparts. You are going to randomly select four male arts athletes and test them whether their vertical jump height exceed (success) or not exceed (failure) twenty-six percentage of the vertical height jump of female martial arts athletes. A) Let x represents the number of four male athletes who exceed twenty-six percentage of the standard vertical height jump of female athletes. Explain why this variable is binomial random variable. B) Find the probability of two of the four male athletes exceed twenty-six percentage of the standard vertical height jump of female athletes. C) Calculate mean and standard deviation of the number of the four male athletes exceed twenty-six percentage of the standard vertical height jump of female athletes. PLEASE show steps and Formula
The integral part of performing arts is ‘Jumping’ that requires strong muscular strength and elasticity of dancers. At what height a dancer vertically jump is one of the measures of dancer’s leg power, and however, it also depends on the level of expertise and amount of training s/he received. A research study conducted among Malaysian undergraduate student martial arts athletes (29 male and 25 female) reports that male arts athletes jump twenty-six percentage higher than their female counterparts. Assume that 90% of male athletes exceed the jump height of female counterparts.
You are going to randomly select four male arts athletes and test them whether their vertical jump height exceed (success) or not exceed (failure) twenty-six percentage of the vertical height jump of female martial arts athletes.
A) Let x represents the number of four male athletes who exceed twenty-six percentage of the standard vertical height jump of female athletes. Explain why this variable is binomial random variable.
B) Find the
C) Calculate
PLEASE show steps and Formula
Given:
n = 4
It is given that 90% of male athletes exceed the jump height of female counterparts.
It means, probability of success p = 0.90
Probability of failure q = 1-p
q = 1-0.90
q = 0.10
Formula Used:
If a random variable X follows Binomial distribution with parameter n and p, then its probability mass function is given by:
If XB(n, p)
P(X = x) = , X = 0, 1, 2, ...n
Mean = np
Standard deviation =
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