Question

State-wide surveys indicate that 14.5% of toddlers in New York are obese. Let the random variable X be the number of toddlers who are obese in a random sample of 20 toddlers from the state of New York.

What is the probability P(X less then or equal too 1)?

a.) 0.0436

b.) 0.1914

c.) 0.1450

d.) 0.0872

Answer 1

Solution

Given that ,

p = 14.5% = 0.145

1 - p = 1 - 0.145 = 0.855

n = 20

x 1

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X1)=P(X=0)+P(X=1)

P(X 1) = ((20! / 0! (20-0)!) * 0.145⁰ * (0.855)^20-0 + ((20! / 1! (20-0)!) * 0.145¹ * (0.855)^20-1

=  ((20! / 0! (20)!) * 0.145⁰ * (0.855)²⁰ + ((20! / 1! (19)!) * 0.145¹ * (0.855)¹⁹

=  0.0436+0.1478

Probability = 0.1914

Option b) is correct.