Consider the following binomial random variables. (a) The number of tails seen i

Question

Consider the following binomial random variables. (a) The number of tails seen in 46 tosses of a quarter (i) Find the mean. (Give your answer correct to one decimal place.) (i) Find the standard deviation. (Give your answer correct to two decimal places.) The number of left-handed students in a dassroom of 48 students assume that 7% of the population is left-handed (G) Find the mean. (Give your answer correct to one decimal place.) i) Find the standard deviation. (Give your answer correct to two decimal places.) e The number of cars found to have unsafe tires among the a07 cars stopped at a roadblock for inspection assume that 19% of all cars have one or more unsafe tires Find the mean. (Give your answer correct to one decimal place.) Find the standard deviation. (Give your answer correct to two decimal places d) The number of melon seeds that germinate when a package of 48 seeds is planted (the package states that the probability of germination is 0.81 (i) Find the mean. (Give your answer correct to one decimal place. (i) Find the standard deviation. (Give your answer correct to two decimal places.) Ask me a

Explanation / Answer

Sol:

For binomial distribution

mean=np

std deviation=sqrt(npq)

p---prob of success

n--no of trials

q---prob of failure

q=1-p

p=1/2

q=1-1/2=1/2

n=46

mean=46*1/2=23

std deviatoon=sqrt(46*1/2*1/2)

=sqrt(11.5)

=3.39

solutionbi:

mean=np=48*0.07

=3.36

solutionbii:

std dev=sqrt(npq)

=sqrt(48*0.07*0.93)

=sqrt(3.1248)

=1.77

Solutionci:

mean=407*19%=407*0.19=77.33

Solutioncii

stddev=sqrt(npq)

=sqrt(407)(0.19)(1-0.19)

=sqrt(62.6373)

=7.91

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