1. 7 During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.
   1. What is the probability of receiving NO calls in a 10-minute period?
   2. What is the probability of receiving more than five calls in a 10-minute period?
   3. What is the probability of receiving less than seven calls in 15-minutes?
   4. What is the probability of receiving at least three but no more than 10 calls in 12 minutes?

USING EXCEL

q3. The probability a car salesman sells a car to a customer is 0.05 Assuming the salesmen sees 12 customers in a week, what is the probability he sells less than 2 cars? Write answer using three decimal places

q4. The Jones family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had: at least 2 girls? at most 2 girls?

A​ gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the​ gender-selection technique,

831831

births consisted of

426426

baby girls and

405405

baby boys. In analyzing these​ results, assume that boys and girls are equally likely.a. Find the probability of getting exactly

426426

girls in

831831

births.b. Find the probability of getting

426426

or more girls in

831831

births. If boys and girls are equally​ likely, is

426426

girls in

831831

births unusually​ high?

c. Which probability is relevant for trying to determine whether the technique is​ effective: the result from part​ (a) or the result from part​ (b)?

d. Based on the​ results, does it appear that the​ gender-selection technique is​ effective?

a.

The

probability of getting exactly

426426

girls in

831831

births is

nothing .

​(Round to four decimal places as​ needed.)

b.

The

probability of getting

426426

or more girls in

831831

births is

nothing .

​(Round to four decimal places as​ needed.)

If boys and girls are equally​ likely, is

426426

girls in

831831

births unusually​ high?

A.

​Yes, because

426426

girls in

831831

births is far from what is​ expected, given the probability of having a girl or a boy.

B.

​Yes, because

426426

girls in

831831

births is not far from what is​ expected, given the probability of having a girl or a boy.

C.

​No, because

426426

girls in

831831

births is far from what is​ expected, given the probability of having a girl or a boy.

D.

​No, because

426426

girls in

831831

births is not far from what is​ expected, given the probability of having a girl or a boy.

c. Which probability is relevant for trying to determine whether the technique is​ effective, the result from part​ (a) or the result from part​ (b)?

A.

The results from part​ (a) and part​ (b) are​ equal, so they are equally relevant.

B.

The result from part​ (b) is more​ relevant, because one wants the probability of a result that is at least as extreme as the one obtained.

C.

Neither of the results are relevant.

D.

The result from part​ (a) is more​ relevant, because one wants the probability of a result that is exactly equal to the one obtained.

d. Based on the​ results, does it appear that the​ gender-selection technique is​ effective?

A.

YesYes​,

because the probability of having

426426

or more girls in

831831

births

isnbsp not nbsp not ​unlikely,

and​ thus,

isnbsp not nbsp not attributable

to random chance.

B.

YesYes​,

because the probability of having

426426

or more girls in

831831

births

isnbsp ​unlikely,

and​ thus,

isnbsp not nbsp not attributable

to random chance.

C.

NoNo​,

because the probability of having

426426

or more girls in

831831

births

isnbsp ​unlikely,

and​ thus,

isnbsp attributable

to random chance.

D.

NoNo​,

because the probability of having

426426

or more girls in

831831

births

isnbsp not nbsp not ​unlikely,

and​ thus,

isnbsp attributable

to random chance.

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To obviate current beach erosion potentials and as a part of beach re-nourishment, Research department’s Dr. Smith proposed a construction of a series of submerged wave energy dissipation structures (=submerged-plate breakwaters) at 110 ft from the shoreline of the Beach. Based on design specifications of the structure, the distribution of the number of waves dissipatable by the proposed structure per hour could be approximated by a normal distribution with a mean of 189 waves and a standard deviation of 7 waves.
1) Use the Empirical Rule to describe the 90% distribution/range of X, i.e., the number
of waves dissipatable by the proposed structure per hour.
2) If the structure is built with dissipating a maximum 195 waves/hour capacity, what
fraction of an hour, i.e., minutes, might the structure be unable to handle incoming
waves (or in other word, how many minutes per hour the structure exceeds 195
waves/hour capacity)?
3) What wave dissipating capacity of the structure should be built so that the
probability of the incoming waves exceeding the structure capacity is equal to only
0.05 (or 5%)?

1. We calculate the total welfare of having health insurance in one case. Suppose the price of hospitalization (i.e. impatient care) is p=500, and suppose the demand function for hospitalization with no insurance is written as q= -0.01p+6, where q is quantity and p is price of hospitalization. One illness might occur with probability of f (=0.4). Suppose one obtains health insurance with a coinsurance rate of 0.2 (no deductible, no stop-loss).

   1. 1) Without health insurance, what is the expected number of hospitalizations?

   2. 2) With health insurance, what is the expected number of hospitalizations?

   3. 3) What is the welfare loss form moral hazard?

   4. 4) What is the expected benefit to be paid by insurance company?

   5. 5) Suppose the loading fee is 20%. What is the insurance premium?

   6. 6) Suppose the risk premium for this risk is $300. How much is the consumer

      willing to pay for this insurance policy?

   7. 7) What is the gain for the consumer?

   8. 8) What is total net welfare (where the welfare gain is the risk reduction, and the welfare cost is moral hazard)? Is there a total net welfare gain or loss?

A) Hypothesis Testing - Type I and Type II errors: You test the claim that the mean gas mileage of all cars of a certain make is less than 29 miles per gallon (mpg). You perform this test at the 0.10 significance level. What is the probability of a Type I error for this test?

B)Sleep: Assume the general population gets an average of 7 hours of sleep per night. You randomly select 40 college students and survey them on their sleep habits. From this sample, the mean number of hours of sleep is found to be 6.69 hours with a standard deviation of 0.40 hours. You claim that college students get less sleep than the general population. That is, you claim the mean number of hours of sleep for all college students is less than 7 hours. Test this claim at the 0.01 significance level.
What is the test statistic? Round your answer to 2 decimal places. t_x=

What is the critical value of t? Use the answer found in the t-table or round to 3 decimal places.
t_α =

1. A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=140+# mg/dl and σ=#+1 mg/dl, where # is the last digit of your student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:
   1. Once?
   2. n=#+2 times, where # is the last digit of your student ID?
   3. n=#+4 times, where # is the last digit of your student ID?
   4. Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.

last number of id is 8