Suppose Students’ scores on the SAT are normally distributed with μ= 1509 and σ= 321

What is the minimum score that would put a student in the top 5% of SAT scores?

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.1 with sample standard deviation s = 1.9. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood

In a large city, the population proportion of residents favoring an increase in electricity price is P = 0.35. A random sample of n = 144. Use p to denote the sample proportion of residents favoring the increase in electricity price.

1. The mean (or expected value) of the sample proportion p is

2. The standard deviation of the sample proportion P is closest to

3. The probability that the sample proportion P is less than or equal to 0.40 is closest to

4. The probability that the sample proportion P is larger than 0.32 is closest to

5. The probability that the sample proportion P is larger than 0.38 is closest to

• Nine observations were selected from each of three populations:    
• (You may think of the rows as weeks)  

a.   What is the value of the Treatment Sum of Squares:………………………..

b.   The value of the Sum of Squares Total:……….. c.   The value of the Error Sum of Squares:…………..

d.   Complete the Anova Table:

e.   State the Null Hypothesis Ho, and the Alternate Ha:

Ho:                                                             Ha:

f.   Do you reject the Null Hypothesis?........................

Consider the following hypotheses:
H₀: μ = 30
H_A: μ ≠ 30

The population is normally distributed. A sample produces the following observations:

At the 10% significance level, what is the conclusion?

a) Reject H₀ since the p-value is greater than α.

b) Reject H₀ since the p-value is smaller than α.

c) Do not reject H₀ since the p-value is greater than α.

d) Do not reject H₀ since the p-value is smaller than α.

Interpret the results αα = 0.1.

a) We conclude that the sample mean differs from 30.

b) We cannot conclude that the population mean differs from 30.

c) We conclude that the population mean differs from 30.

d) We cannot conclude that the sample mean differs from 30.

A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 2.6. (Round your answers to two decimal places.)

(a) Compute a 95% CI for μ when n = 25 and x = 56.2.

(_____,______) watts

(b) Compute a 95% CI for μ when n = 100 and x = 56.2.
(_____,______) watts
(c) Compute a 99% CI for μ when n = 100 and x = 56.2

(_____,______) watts.

(d) Compute an 82% CI for μ when n = 100 and x = 56.2.

(_____,______) watts

(e) How large must n be if the width of the 99% interval for μ is to be 1.0? (Round your answer up to the nearest whole number
n = _____

A cyclist won a bicycle race for seven consecutive years. His "winning" times and "victory" margins (time difference of the second place finisher) are given in the figure below.

(a) Find the mean, median and mode of the cyclist's times. (If an answer does not exist, enter DNE.)

(b) Find the mean, median and mode of the cyclist's margins. (If an answer does not exist, enter DNE.)

A random sample of 29 pairs of observation from a normal population gives correlation coefficient of 0.64. Is it likely that variables in the population are uncorrelated at 5% L.O.S?

When you purchase a car, you may consider buying a brand-new car or
a used one. A fundamental trade-off in this case is whether you pay
repair bills (uncertain at the time you buy the car) or make loan payments
that are certain.
Consider two cars, a new one that costs $15,000 and a used one with
75,000 miles for $5,500. Let us assume that your current car’s value and
your available cash amount to $5,500, so you could purchase the used car
outright or make a down payment of $5,500 on the new car. Your credit
union is willing to give you a five-year, 10% loan on the $9,500 difference
if you buy the new car; this loan will require monthly payments of $201.85
per month for 5 years. Maintenance costs are expected to be $100 for the
first year and $300 per year for the second and third years.
After taking the used car to your mechanic for an evaluation, you
learn the following. First, the car needs some minor repairs within the
next few months, including a new battery, work on the suspension and
steering mechanism, and replacement of the belt that drives the water
pump. Your mechanic has estimated that these repairs will cost $150.
Considering the amount you drive, the tires will last another year but will
have to be replaced next year for about $200. Beyond that, the mechanic
warns you that the cooling system (radiator and hoses) may need to be
repaired or replaced this year or next and that the brake system may need
work. These and other repairs that an older car may require could lead
you to pay anywhere from $500 to $2,500 in each of the next 3 years. If
you are lucky, the repair bills will be low or will come later. But you
could end up paying a lot of money when you least expect it.

Draw a decision tree for this problem. To simplify it, look at the situation
on a yearly basis for 3 years. If you buy the new car, you can
anticipate cash outflows of 12 × $201.85 = $2,422.20 plus maintenance
costs. For the used car, some of the repair costs are known (immediate
repairs this year, tires next year), but we must model the uncertainty
associated with the rest. In addition to the known repairs, assume that in
each year there is a 20% chance that these uncertain repairs will be $500,
a 20% chance they will be $2,500, and a 60% chance they will be
$1,500. (Hint: You need three chance nodes: one for each year!)
To even the comparison of the two cars, we must also consider their
values after 3 years. If you buy the new car, it will be worth approximately
$8,000, and you will still owe $4,374. Thus, its net salvage value
will be $3,626. On the other hand, you would own the used car free
and clear (assuming you can keep up with the repair bills!), and it
would be worth approximately $2,000.
Include all of the probabilities and cash flows (outflows until the
last branch, then an inflow to represent the car’s salvage value) in your
decision tree. Calculate the net values at the ends of the branches.

1. A study of sterility in the fruit fly reports the following data on the number of ovaries developed by each female fly in a sample of size 1386. One model for unilateral sterility states that each ovary develops with some probability p independently of the other ovary. Test the fit of this model using χ². (Use α = 0.05.)

Calculate the test statistic (Round your answer to two decimal places

2. The accompanying data refers to leaf marks found on white clover samples selected from both long-grass areas and short-grass areas. Use a χ² test to decide whether the true proportions of different marks are identical for the two types of regions. (Use α = 0.01.)

Type of Mark

Calculate the test statistic (Round your answer to two decimal places)

z

Q3. A sample of single persons in Towson, Texas, receiving Social Security payments
revealed these monthly benefits: $852, $598, $580, $1,374, $960, $878, and $1,130.
(a) What is the median monthly benefit?
(b) How many observations are below the median? Above it?

Each student taking the probability calculus exam draws a card from 2 out of 40 different questions. In order to pass the exam, you have to answer both questions from the card or one question from the card and an additional question indicated by the examiner from another card. Max went to the exam, but knew the answer to only 33 questions. Calculate the probability that Max

(a) he passed the exam,
(b) answered both questions from a drawn sheet of card, if known to have passed the examination.
(c) answered one question on a drawn sheet of card if known not to have passed the examination.

Statistics

EXERCISE 17. A die is cast three times. What is the probability a) of not getting three 6´s in succession? b) that the same number appears three times? Answer. a) 215/216. b) 6/216.

EXERCISE 18. A die is thrown three times. What is the probability a) that the sum if the three faces shown is either 3 or 4? b) that the sum if the three faces shown is greater than 4? Answer. a) 4/216. b) 212/216.

EXERCISE 19. A hunter fires 7 consecutive bullets at an angry tiger. If the probability that 1 bullet will kill is 60%, what is the probability that the hunter is still alive? Answer. 99,83616%.

EXERCISE 20. According to the U. S. Census Bureau, 62% of Americans over the age of 18 are married. Find the probability of getting two married people (not necessarily to each other) when two different Americans over the age of 18 are randomly selected. Answer. 38,4%.

EXERCISE 21. A Roper poll showed that 18% of adults regularly engage in swimming. If three adults are randomly selected, find the probability that they all regularly engage in swimming. Answer. 0,583%.

EXERCISE 22. Four firms using the same auditor independently and randomly select a month in which to conduct their annual audits. What is the probability that all four months are different? Answer. 55/96.

Please show your workings. I have provide you with the possible answers. Some of them might be wrong though. If there is not gonna be enough space you can show your working on a picture. Thank you in advance!