Respuesta :
Answer:
[tex]P(x< 175)= 0.9772[/tex]
Explanation:
given,
mean weight of human = μ = 170 lbs
standard deviation = SD = 50 lbs
N = 400 humans
By using central limit theorem,
P (x< 175)
[tex]P(x< 175)= P(z<\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]
[tex]P(x< 175)= P(z<\dfrac{175 -170}{\dfrac{50}{\sqrt{400}}})[/tex]
[tex]P (x< 175)= P(z<\dfrac{5}{2.5}))[/tex]
[tex]P (x< 175)= P(z<2)[/tex]
using z-table
[tex]P (x< 175)= 0.9772[/tex]
hence, the probability that total weight is less tan 175 lbs is equal to
[tex]P(x< 175)= 0.9772[/tex]
