c. Find the probability that at least one worker from each state belongs to a un

Question

c. Find the probability that at least one worker from each state belongs to a union Public Health and Nutrition A recent report suggests that one-third of all U.S. children are overweight or obese, One possible cause is the availability of junk foods and sugary snacks in schools. Approximately 40% of all students buy and eat one or more snacks in schools.^25 Suppose 40 school children are selected at random. a. Find the mean, variance, and standard deviation of the number of school children (out of the 40 selected) who buy and eat a snack at school. b. Construct intervals one, two, and three standard deviations form the mean. C. Suppose 27 students (out of the 40 selected) buy and eat snack at school. How many standard deviations from the mean is this observation? What does this distance measure indicate about the likelihood of observing 27 students who buy and eat a snack at school?

Explanation / Answer

it is given that approximately 40% of all students buy and eat one or more snacks at school.

40 school children selected at random

let X be the random variable denoting the number of school children out of 40 children who buy and eat snacks at school.

so X~Bin(40,0.4)

a) mean is E[X]=40*0.4=16 [answer]

variance is V[X]=40*0.4*(1-0.4)=9.6 [answer]

standard deviation is s=sqrt(9.6)=3.098 [answer]

b) interval of one standard deviation from mean is

[16-3.098,16+3.098]=[12.902,19.098]

interval of two standard deviation from mean is
[16-3.098*2,16+3.098*2]=[9.804,22.196]

interval of three standard deviation from mean is
[16-3.098*3,16+3.098*3]=[6.706,25.294]

c) it is observed that 27 students buy and eat snacks from school.

let 16+3.098*k=27

or, k=(27-16)/3.098=3.55

hence this observation is 3.55 standard deviations from the mean

so it seems that the distance measure is quite high.

most of the values lie within the three standard deviation from mean interval

but 27 lies outside that interval

hence this measure distance indicates that the likelihood of observing 27 students is very low and unlikely

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.