Study shows that 30% of college students carpool to school. If we randomly selec

Question

Study shows that 30% of college students carpool to school. If we randomly select 80 college students, find The mean number of students that carpool to school. The standard deviation for the number of students that carpool to school. Use normal distribution to estimate the probability that there will be at most 20 students that carpool to school. Use normal distribution to estimate the probability that the number of college students that carpool exceed 20. Use normal distribution to estimate the probability that the number of college students that carpool is between 20 and 30 inclusive.

Explanation / Answer

Part-a

Mean number of students that carpool to school =np=80*0.30 =24

Part-b

Standard deviation of students that carpool to school=sqrt(np(1-p)) =sqrt(80*0.30*(1-0.30)) =4.10

Part-c

Using normal distribution X, the students that carpool to school, we have x follows normal distribution with mean=24 and standard deviation sigma=4.10

So, using continuity correction,

P(X<=20)= P(X<20.5)

=0.1966, using excel function =NORMDIST(20.5,24,4.1,TRUE)

Part-d

So, P(X>20)=1-P(X<=20)=1-0.1966= 0.8034

Part-e

P(20<=X<=30)=P(X<=30)-P(X<20)

=P(X<30.5)-P(X<19.5)

=0.9436-0.1362

=0.8074 , using excel functions =NORMDIST(30.5,24,4.1,TRUE) and =NORMDIST(19.5,24,4.1,TRUE)

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