The mean cost of domestic airfares in the United States rose to an all-time high of $375 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $100. Use Table 1 in Appendix B. a. What is the probability that a domestic airfare is $550 or more (to 4 decimals)? b. What is the probability that a domestic airfare is $265 or less (to 4 decimals)? c. What if the probability that a domestic airfare is between $310 and $480 (to 4 decimals)? d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)

The weights of a certain brand of candies are normally distributed with a mean weight of

0.85960.8596

g and a standard deviation of

0.05240.0524

g. A sample of these candies came from a package containing

440440

​candies, and the package label stated that the net weight is

375.5375.5

g.​ (If every package has

440440

​candies, the mean weight of the candies must exceed

StartFraction 375.5 Over 440 EndFraction375.5440equals=0.85340.8534

g for the net contents to weigh at least

375.5375.5

​g.)

PLEASE GIVE A VERY DETAILED ANSWER AS I HAVE TO WRITE A 2 PAGE PAPER!!!

Summarize the main points of the central limit theorem.

Discuss the advantages and disadvantages to having a large sample size in a research setting.

Explain whether or not you believe applying the central limit theorem always justifies having a sample large enough to do so, providing examples when possible.

A worldwide organization of academics claims that the mean IQ score of its members is 118 , with a standard deviation of 15 . A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 115.2 . If the organization's claim is correct, what is the probability of having a sample mean of 115.2 or less for a random sample of this size? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 14 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized? (Round your answer to 2 decimal places.)

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective.

Step 2 of 2 :  

Suppose a sample of 1536floppy disks is drawn. Of these disks, 1383 were not defective. Using the data, construct the 98% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. Construct a 99​% confidence interval estimate of the mean​ drive-through service time for Restaurant X at​ dinner; then do the same for Restaurant Y. Compare the results. LOADING... Click the icon to view the data on​ drive-through service times. Construct a 99​% confidence interval of the mean​ drive-through service times at dinner for Restaurant X.

Restaurant X   Restaurant Y
83   104
117   123
115   156
142   117
263   171
180   136
121   112
151   124
162   125
217   127
331   129
303   134
177   232
109   212
157   291
150   125
92   99
233   137
235   242
185   145
155   142
195   202
168   146
120   145
67   134
197   144
174   161
117   131
146   172
175   130
193   240
199   237
227   254
192   239
347   237
305   172
215   85
195   105
182   52
186   175
102   81
143   143
180   141
152   97
176   128
153   149
168   131
125   189
137   154
312   131

Suppose a simple random sample of size n=64 is obtained from a population with μ=76 and σ=8.

​(a) Describe the sampling distribution of x̅

​(b) What is P (x̅ > 77.7)?

​(c) What is P (x̅ ≤ 73.65)?

​(d) What is P (74.5 < x̅ < 78.15)?

A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 40 cables and apply weights to each of them until they break. The 40 cables have a mean breaking weight of 775.3 lb. The standard deviation of the breaking weight for the sample is 14.9 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable. ( , ) Your answer should be rounded to 2 decimal places.

1. Two golf balls are selected with replacement from a bowl containing 7 red and 3 blue balls
   1. What is the probability that both balls are red?
   2. What is the probability that both balls are blue?
   3. What is the probability that the first ball is red and the second ball is blue?
   4. What is the probability that the first ball is blue and the second ball is red?
   5. What is the probability that the two balls selected are the same color?
2. Adam goes to the grocery store. Suppose probability he buys milk is 40%, and the probability he buys steak is 70%, and the probability of both is 30%. What is the probability that he buys either milk or steak?
3. A car dealer has had issues with new cars that are being delivered with flawed paint and tires that are one too small. The two assembly shops are not related to one another. If the probability of flawed paint is 5% and the probability of the wrong size tire is 8%, then what is the probability that the next car delivered will have flawed paint and too small tires?

Information for Problems 1 - 5: Photoresist is a light sensitive material used in industrial processes like photolithography and photoengraving to form a patterned coating on a surface. There are two types of photoresists: positive and negative. A positive photoresist is one in which the portion of the photoresist that is exposed to light becomes soluble to the photoresist developer. A negative photoresist is one in which the portion of the photoresist that is exposed to light becomes insoluble to the photoresist developer. Suppose the thickness, x, of photoresist applied to wafers in semiconductor manufacturing at a particular location on the wafer is uniformly distributed between 0.2150 and 0.2350 micrometers.

1.     Find the probability distribution function for x.  

2.     Find the cumulative distribution function of photoresist thickness.

3.     Determine the proportion of wafers that exceed 0.2275 micrometers in photoresist thickness.

4.     What is the minimum thickness that is exceeded by 30% of the wafers?   

5.     Determine the mean of the photoresist thickness.

Information for Problems 6 - 10: Cholesterol is a fatty substance that is an important part of the outer lining (membrane) of cells in the body of animals. Its normal range for an adult is 120-240 mg/dl. The Food and Nutrition Institute (FNI) of the Philippines found that the total cholesterol level for Filipino adults has a mean, µ, of 148.9 mg/dl. Furthermore, the FNI reports that 92% of adults have a total cholesterol level below 200 mg/dl and that total cholesterol level is normally distributed.

6.     What is the standard deviation of this normal distribution? Give answer to 1 decimal places.

7.     An adult is considered to be at high risk for cardiovascular disease if his/her total cholesterol level is above 240.8 mg/dl. What proportion of Filipino adults are at high risk for cardiovascular disease? Give answer to 4 decimal places.

8.     An adult is considered to be at moderate risk for cardiovascular disease if his/her total cholesterol level is between 200 and 240.8 mg/dl. What proportion of Filipino adults are at moderate risk for cardiovascular disease?   Give answer to 4 decimal places.

9.     What is the value of total cholesterol level that exceeds 90% of the Filipino population? Give answer to 2 decimal places.

10. Above what total cholesterol value will 25% of the Filipino population fall? Give answer to 2 decimal places.

Information for Problems 11 - 15: A fiber spinning process currently produces a fiber whose strength is normally distributed with a mean of 71 N/m². The minimum acceptable strength is 65N/m². Give answer to 4 decimal places.

11. Ten percent of the fiber produced by the current method fails to meet the minimum specification. What is the standard deviation of the fiber strengths in the current process?   

12. If the mean remains at 71N/m² and the minimum acceptable strength remains at 65N/m², what must the standard deviation be so that only 5% of the fiber will fail to meet the specification?

13. If the mean remains at 71N/m² and the minimum acceptable strength remains at 65N/m², what must the standard deviation be so that only 1% of the fiber will fail to meet the specification?

14. If the standard deviation is 3N/m², to what value must the mean be set so that only 1% of the fiber will fail to meet the minimum specification of 65N/m²?

15. If the standard deviation is 3N/m², to what value must the mean be set so that only 2% of the fiber will fail to meet the specification of 65N/m²?