Answer :
111.51 is the probability of the random sample of 15 people that 4 of them are left-handed.
P(exactly x out of n) = (n! ÷ (x! × (n - x)!)) × [tex]p^{x}[/tex] × [tex](1 - p)^{n - x}[/tex].
where n = number of trials = 15.
p = probability of selecting one lefty in one trial = 10% or 0.1
x = probability which needs to be deduced = 4.
P(exactly 4 out of 10) = (10! ÷ (4! × (10 - 4)!)) × [tex]1^{4}[/tex] × [tex](1 - 0.1)^{10 - 4}[/tex].
P(exactly 4 out of 10) = (10! ÷ (4! × 6!)) × [tex]1^{4}[/tex] × [tex](0.9)^{6}[/tex].
P(exactly 4 out of 10) = 210 × [tex]1^{4}[/tex] × [tex](0.9)^{6}[/tex].
P(exactly 4 out of 10) = 210 × 1 ×0.531
P(exactly 4 out of 10) = 111.51
The probability that 4 of them are left-handed is 111.51.
Learn more about the normal distribution at
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