Question

4.3% of the products in a warehouse are damaged. a. If 10 products are randomly selected from the warehouse, what is the probability that exactly one of them is damaged? Use formulas. b. If 10 products are randomly selected from the warehouse, what is the probability that at least one is damaged? Use your calculator. (State the calculator command used.) c. State the mean and standard deviation for the number of damaged products in groups of size 10 from that warehouse. d. Use the range rule of thumb to approximate significantly high and low numbers of damaged products in groups of size 10 from that warehouse.

Answer 1

here this is binomial with parameter n=10 and p=0.043

a)

probability that exactly one of them is damaged =P(X=1)=(₁₀C₁)*0.043¹(1-0.043)⁹ =0.2895

b)

probability that at least one is damaged =P(X>=1) =1-P(X=0)=1-0.6443 =0.3557

for ti-84 : you can use command (1-binompdf(10,0.043,0))

c)

mean E(x)=μ=np=0.43

standard deviation σ=√(np(1-p))=0.6415

d)

significantly high value =2 standard deviation above mean value =0.43+2*0.6415 =1.713

significantly low value =2 standard deviation below mean value =0.43-2*0.6415 =-0.853 ~ 0.000