Books from a certain publisher contain on average 1 misprint per page. Suppose those misprints occur according to a Poisson scatter, with a rate on 1 per page. One of the books from this publisher has 200 pages.

(a). What is the probability that there are at least 70 pages in this book with no misprints?

(b). What is the probability that there is at least one page in this book with 5 or more misprints?

(c). Suppose a proofreader goes through this book and catches each misprint with probability 0.7 (independently for different misprints). If the caught misprints are fixed, what is the probability that there are still 60 or more pages containing misprints?

(d). If this proofreader catches 3 misprints on a page, what is the probability that there are still misprints that weren't caught on that page?

1.) Suppose heights of two-year-olds are normally distributed with a mean of 30 inches and a standard deviation of 3.5 inches.

a) What is the probability that one two-year-old will be shorter than 28 inches?

b) If random samples of size n = 40 two-year-olds are selected, what is the approximate shape, mean, and standard deviation of the sampling distribution of sample means?

c) What is the probability that the sample mean of these 40 two-year-olds will be shorter than 28 inches? Why is the probability in part c) so much smaller than the probability in part a)?

d) What is the probability that the sample mean of these 40 two-year-olds will be taller than 31 inches?

Here is the probability model for the blood type of a randomly chosen person in the United States.

(a) What is the probability that a randomly chosen American has type AB blood? Please use 2 decimal places.


(b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen American can donate blood to Maria? Please use 2 decimal places.


(c) What is the probability that a randomly chosen American does not have type O blood? Please use 2 decimal places.

According to the bureau of labor statistics, it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers. Assume that the probability distributions are normal and that the standard deviation is 2 weeks for both distributions.

A) What is the probability that it takes a worker over the age of 55 more than 19 weeks to find a job?

B) What is the probability that it takes a younger worker more than 19 weeks to find a job?

C) What is the probability that it takes a worker over the age of 55 between 23 and 25 weeks to find a job?

D) What is the probability that it takes a younger worker between 23 and 25 weeks to find a job?

6) Given a variable with the following population parameters: Mean = 20 Variance = 16
a) What is the probability of obtaining a score greater than 23?
b) What is the probability of obtaining a score greater than 16?
c) What is the probability of obtaining a score less than 10?
d) What is the probability of obtaining a score greater than 18 and less than 21? e) What is the probability of obtaining a score greater than 21 and less than 27? f) What is the score at which 75% of the data falls at or below?
g) What is the score at which 22% of the data falls at or above?
h) Within what two scores do 95% of the scores fall (i.e. symmetrically)?

The classrooms at the Redman Academy consist of cramped tables that seat 3 people. The probability of being-left handed is 26%, and left-handed test takers need to sit in the far-left seat, otherwise, they constantly bump elbows with the person next to them causing complaints.   
⦁   What is the probability that no one in a group of 3 students is left-handed?
⦁   What is the probability that only 1 person in the group of 3 students is left-handed?
⦁   What is the probability that no one at a table will complain during a test if I randomly seat three students?
⦁   I have 9 students in my class, 2 of which are left-handed. If I have exactly 3 tables and randomly seat the students, what is the probability of no complaints?

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.192.

Consider your next 34 purchases that produce a game piece. Calculate the following:

This is a binomial distribution. Round your answers to 4 decimal places.

a) What is the probability that you win 7 prizes?

b) What is the probability that you win more than 9 prizes?

c) What is the probability that you win between 4 and 7 (inclusive) prizes?

d) What is the probability that you win 5 prizes or fewer?

The Titanic Used the data in the following table, which summarizes results from the sinking of the titanic.

1. If one of the Titanic passengers is randomly selected, find the probability of getting someone who is a women or survivor.
2. If one of the Titanic passengers is randomly selected, find the probability of getting a man and someone who survived the sinking.
3. If one of the Titanic passengers is randomly selected, find the probability of getting a boy or girl?
4. If one of the Titanic passengers is randomly selected, find the probability of getting a man, given that the selected person died.
5. If Three of the Titanic passengers is randomly selected, find the probability of all three are boys?

According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123]

Compute the probability that a randomly selected peanut M&M is not yellow.



Compute the probability that a randomly selected peanut M&M is green or yellow.



Compute the probability that two randomly selected peanut M&M’s are both red.



If you randomly select five peanut M&M’s, compute that probability that none of them are green.



If you randomly select five peanut M&M’s, compute that probability that at least one of them is green.

1. A species of flowering plant includes plants with blooms that range from bright golden yellow to very pale yellow; no flowers carrying the yellow pigment allele appear white. The allele for yellow flower color:

a. must be a suppressor of another allele.
b. demonstrates incomplete penetrance.
c. demonstrates variable expressivity.
d. must be a modifier of another allele.
e. demonstrates variable penetrance.

2. Coat color in mice is determined by two alleles acting at a single locus: B is dominant and results in mice with black coats, and b is recessive and results in mice with white coats. In a litter of 12 mice, nine are black (B/–) and three are white (b/b). What is the penetrance of the B coat color allele?

a. zero
b. 25 percent
c. 50 percent
d. 75 percent
e. 100 percent

3. Semisterility in nearly 50 percent of the progeny they produce is often an indication that:

a. the parents are translocation heterozygotes.
b. both parents carry pericentric inversions.
c. both parents carry polytene chromosomes.
d. one of the parents carries a chromosomal deletion that removes a telomere.
e. one of the parents carries a chromosomal deletion that removes a chromosome's centromere.

4. A researcher is studying melanoma cells derived from a patient's skin tumor. He determines that all melanoma cells are 2n + 1, but the chromosome number in all normal skin cells is 2n. The 2n + 1 melanoma cells likely arose from:

a. mitotic nondisjunction.
b. meiotic nondisjunction.
c. mitotic recombination.
d. parthenogenesis.
e. colchicine treatment.

5. Why won't a balancer chromosome in Drosophila produce viable crossover products when paired with a wild-type chromosome?

a. Balancer chromosomes contain multiple inversions.
b. Balancer chromosomes contain multiple deletions.
c. Balancer chromosomes have no centromere.
d. Balancer chromosomes have no telomeres.
e. None of the answers is correct.

6. A doctor notes that a patient's genome contains 100 potentially harmful recessive mutations; however, the patient is heterozygous for all of the loci considered and thus does not demonstrate any abnormal phenotypes. The 100 recessive mutations the doctor discovered represent the patient's:

a. bivalents.
b. monosomy.
c.genetic load.
d. amphidiploidy.
e.nondisjunction.

7.The term describing the relationship between the number of copies of a gene and how much product is made from the gene is:

gene-dosage effect.
gene balance.
dosage compensation.
transcription.
aneuploidy.

8. The gene for upright ears in rabbits has two alleles. The E allele is dominant and results in upright ears, and the recessive e allele results in droopy ears. Of 100 rabbits surveyed, 87 had a genotype for upright ears (E/–). However, only 72 of these 87 rabbits had upright ears; the remaining 15 rabbits had completely droopy ears. This suggests that the allele for upright ears:

a. has incomplete penetrance.
b. has complete penetrance.
c. demonstrates variable expressivity.
d. is lethal.
e. is incompletely dominant.

9. A researcher has selfed an autotetraploid plant with the genotype D/D/d/d, and in the resulting progeny she observes a 35:1 phenotypic ratio. What can she conclude from this observation?

a. The progeny from this cross do not demonstrate a standard Mendelian phenotypic ratio.
b. In the 35:1 phenotypic ratio, the 1 represents the phenotype of the d/d/d/d progeny.
c. During meiosis in the D/D/d/d parent plant, it is likely that only bivalents, no quadrivalents or trivalents, formed.
d. It is likely that in this plant species, gametes associate with one another randomly.
e. All of the answers are correct.

10. A researcher is studying fur color in a new species of bats. He notices that fur color, which is due to the presence of a dominant allele (G), ranges from light gray to very dark gray. In addition, some bats that carry a G allele have no fur pigmentation whatsoever; their coats appear white. This is an example of:

a. only variable expressivity.
b. only incomplete penetrance.
c. both variable expressivity and incomplete penetrance.
d. recessive allele lethality.
e. pleiotropy.