Two boys and three girls enter a music hall and take five seats at random in a row.

1) How many different ways can they sit in a row?

2)What is the probability the girls will take the end two seats?

3) What is the probability that the boys will sit together and the boys will sit together?

4)How many different ways can they sit alternately, like BGBGB or GBGBG

5) How many different ways can they sit if the seats are arranged in a circle?

Suppose a Department Chair randomly selects 5 new teaching assistants from a total of 20 applicants - 11 boys and 9 girls. Let x be the number of girls who are hired. Find the mean and standard deviation of random variable x.

(a) μ = 2.75 and σ = 0.9770

(b) μ = 2.25 and σ = 0.9884

(c) μ = 2.75 and σ = 0.9884

(d) μ = 2.25 and σ = 0.9770

1. For the andorian species, if the probability that a couple produces a girl is 0.97193, and if the couple has 8 children, what is the probability they will have:
5 boys and 3 girls (in any order)?

2. For the Vulcan species, if the probability that a couple produces a girl is 0.23477, and if the couple has 5 children, what is the probability they will have:
3 boys and 2 girls (in any order)?

You are expected to prepare a human pedigree detailing the inheritance of a single
genetic disease or disorder.
The pedigree will be created from the following information:
● There are five generations.
● In generation 1, there are two families.
o family one, the male is affected; this family should be listed on the
left.
o family 2 the female is affected.
● In generation 2 there are 12 individuals. Information on this generation:
o family 1 had 7 children, family 2 had four.
o family 1 first three children were girls, the remainder boys
o family 2 had a girl, two boys, and another girl.
o the eldest female of family 1 was married.
▪ She went on to have one daughter, and then one male,
affected
o the youngest male of family 1 and the eldest female of family 2
were married. This youngest male was affected.
▪ They went on to have five children. One girl, two boys, and
two more girls. The eldest boy, and two youngest girls were
all affected.
▪ The eldest daughter went on to have a boy and a girl.
o the youngest daughter of family 1, and both males of family 2, were
affected.
● In generation 3 there are at least 9 members.
o The youngest girl of the merged family had two sons. The first died
at birth and it is unknown if he was affected. The second was
affected
o The second oldest daughter of the merged family had one affected
male. She was not married.
o A daughter was born, who was a descendant of family 1 only,
whose mother was unaffected
▪ Her father was affected.
▪ She also has an adopted brother
▪ She went on to have twin daughters
▪ She was not married
● In generation 4 there are 7 members.
o Four of five males were affected
● In generation 5 there are 2 members.
● Generation one is dead.
● Non-married partners are not included in the pedigree.
● Unless specified assume all individuals have married parents.
● Unless specified, assume all spouses are unaffected
You will provide all genotypes for the second generation and ensure all known affected
individuals are marked.

After depicting the disease on the pedigree, you should include determine its dominant
or recessive inheritance pattern, and its autosomal or sex-linked position in the human
genome. Then, you will research a condition that matches this pattern and describe it in
full. Also, you should include a brief description of the manifestations and clinical
outcomes of the disease. The written portion of the assignment should be completed in
Microsoft Word.

As technology advances, teenagers who are online become more exposed and easier to find despite privacy measures. In a random sample, girls were less likely than boys to say that they are easy to find online from their profiles. Of 268 teenage boys with profiles, 75 say that they are easy to find online from their profiles, while out of 325 girls, 62 say they are easy to find online from their profiles.

Create a 95% confidence interval for the difference in the proportion of teenage boys who say that they are easy to find online from their profiles and that of teenage girls who say that they are easy to find online from their profiles.

Perform a hypothesis test that reflects the original aim of the experiment, at the 5% level of significance.

 A statistician for a drug company wishes to determine whether short-term memory scores are affected by the type of medication in hyperactive children. Sixty hyperactive children (30 boys and 30 girls) were randomly assigned to receive either Cylert or Ritalin (two kinds of amphetamines which are CNS stimulants). Their short-term memory was tested on a 20-point scale (where 0 = no memory and 20 = perfect memory).
 

Boys Cylert: 12, 10, 13, 10, 9, 12, 13, 10, 11, 12
Boys Placebo: 5, 6, 7, 6, 4, 5, 6, 7, 5, 7
Boys Ritalin: 3, 2, 5, 6, 1, 4, 2, 6, 1, 5
Girls Cylert: 5, 6, 2, 4, 3, 2, 4, 6, 2, 4
Girls Placebo: 4, 6, 7, 6, 5, 4, 5, 6, 7, 7
Girls Ritalin: 12, 9, 14, 13, 9, 12, 8, 15, 12, 11

solve for degrees of freedom, sum of squares and f values

a) For the production of a local play, 8 people auditioned and 6 of them joined the cast. Of these, 4 had named roles. In how many ways could this have happened?

b) In how many ways can 55 boys and 55 girls be arranged in a circle so that the boys and girls are alternating

c) How many 55-digit numbers have the property that the first and last digits are different?