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Answer:
d) The highest probability occurs when x equals 0.7500
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability, given by the following formula:
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
In this problem, we have that:
a) The standard deviation is 0.8441
This is correct
b) The number of trials is equal to 15
n is the number of trials and . So this option is correct.
c) The probability that x equals 1 is 0.3658
This option is correct.
d) The highest probability occurs when x equals 0.7500
False. The number of sucesses is a discrete number, that is, 0, 1, 2,...,15. P(X = 0.75), for example, does not exist.
e) The mean equals 0.7500
This option is correct.
f) None of the above
d is false