Question

A study by the Centers for Disease Control and Prevention (Use of Medication Prescribed for Emotional or Behavioral Difficulties Among Children Aged 6–17 Years in the United States, 2011–2012,, by LaHeana Howie et al., NCHS Data Brief Number 148, April 2014 showed that 7.5% of children ages 6–17used prescribed medication during the past six months for emotional or behavioral difficulties. The binomial experiment is to select four children ages 6–17 random, and to find the probability that X takes the following values, where X equals the number of children using prescription medication for emotional or behavioral difficulties.

(Use decimal notation. Give your answers to six decimal places.)

?(?=3)=

?(?≥3)=

?(?=0)=

?(?≤1)=

?(1≤?≤4)=

?(1<?<4)=

Answer 1

Here we can use Binomial distribution with n=4 children and probability = p=7.5%=0.075

We use Excel formula '' BINOMDIST( number_success, number_trial, prob_success, cumulative )'' to calculate probability.

P(X=3)=0.001561 ======>>>>Use excel function ''=BINOMDIST(3,4,0.075,FALSE)''

P(X>=3)=1-P(X<=2)

=1-0.998407 ======>>> Use ''=BINOMDIST(2,4,0.075,TRUE)''

=0.001593

P(X=0)=0.732094 ======>>>use ''=BINOMDIST(0,4,0.075,FALSE)''

P(X<=1)=0.969530 =====>>>use ''=BINOMDIST(1,4,0.075,TRUE)''

P(1<=X<=4)=P(X<=4)-P(X<=1)

=1-0.969530

=0.030469

P(X1<X<4) =P(X<=3)=P(X<=0)

=0.999968-0.732094

=0.267874

Hope this will be helpful. Thanks and God Bless You :)