Answer:
0.1971 ( approx )
Step-by-step explanation:
Let X represents the event of weighing more than 20 pounds,
Since, the binomial distribution formula is,
[tex]P(x)=^nC_r p^r q^{n-r}[/tex]
Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Given,
The probability of weighing more than 20 pounds, p = 25% = 0.25,
⇒ The probability of not weighing more than 20 pounds, q = 1-p = 0.75
Total number of samples, n = 16,
Hence, the probability that fewer than 3 weigh more than 20 pounds,
[tex]P(X<3) = P(X=0)+P(X=1)+P(X=2)[/tex]
[tex]=^{16}C_0 (0.25)^0 (0.75)^{16-0}+^{16}C_1 (0.25)^1 (0.75)^{16-1}+^{16}C_2 (0.25)^2 (0.75)^{16-2}[/tex]
[tex]=(0.75)^{16}+16(0.25)(0.75)^{15}+120(0.25)^2(0.75)^{14}[/tex]
[tex]=0.1971110499[/tex]
[tex]\approx 0.1971[/tex]
