8. The amounts of nicotine in a certain brand of cigarette have a normal distribution with a mean of 0.909 g and a standard deviation of 0.317 g.

The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 43 cigarettes with a mean nicotine amount of 0.817 g.

Assuming that the given mean and standard deviationhave NOT changed, find the probability of randomly selecting 43 cigarettes with a mean of 0.817 gor less.

P(Sample Mean 0.817 g) = P(X0.817)P(X0.817) =

Enter your answer as a number accurate to 4 decimal places.

Assume that any probability below 5% is sufficient to conclude that the new product really has lower nicotine. Based on the result above, is it valid to claim that the amount of nicotine is lower?

• Yes. The probability of this data is unlikely to have occurred by chance alone.
• No. The probability of obtaining this data is high enough to have been a chance occurrence.

9. Which of the following statements are true?

I. The sampling distribution of xx has standard deviation nn even if the population is not normally distributed.

II. The sampling distribution of xx is normal if the population has a normal distribution.

III. When nn is large, the sampling distribution of xx is approximately normal even if the the population is not normally distributed.

• I and II
• I and III
• II and III
• I, II, and III
• None of the above gives the complete set of true responses.

10. According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3326 grams and a standard deviation of 583 grams.

1. What is the probability that a randomly selected baby weighs between 3200 grams and 3500 grams? Round your answer to 4 decimal places.
2. What is the probability that the average weight of 16 randomly selected babies is between 3200 grams and 3500 grams? Round your answer to 4 decimal places.
3. Why did the probability increase?

• The probability increased since the sample size increased and the sample means are more concentrated near the mean of 33263326.
• The probability increased since the sample size increased and the distribution of sample means is more spread out.

12.

Delivery times for shipments from a central warehouse have a right skewed distribution with a mean of 2.06 days (note that times are measured continuously, not just in number of days) and a standard deviation of 2.06 days.

A random sample of 99 shipments are selected and their shipping times are observed.

1. Use the Central Limit Theorem to find the probability that themeanshipping time for the 99 shipments is less than 1.79 days.
2. Round your answer to 4 decimal places.
3. If5% is the highest probability for an unusual occurrence, using your computed probability above, would you say this sample of shipments was unusual?

• Not unsual, because computed probability is higher than 0.05.
• Yes, because computed probability is NOT higher than 0.05.

10. The daily production of a herd of cows has a normal distribution.

What is the probability that the production of a herd of cows on a randomly selected day will be within 1.05 standard deviations of its mean?

Provide answer with 4 or more decimal places.

5. CNNBC recently reported that the annual cost of auto insurance has a mean of 1002 and a standard deviation of 282.

A random sample of 10 auto insurance policies is selected and consider themean cost of this sample.

What is the mean of its distribution?

What is the standard error of its distribution?

6. Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 185000 dollars. Assume the standard deviation is 42000 dollars.

Enter each answer as a number between 0 and 1 accurate to 4 decimal places.

a. Find the probability that salary of a randomly selctedsinglegraduate is more than 179000 dollars.

P(X> 179000) =

b. Suppose you take a simple random sample of 80 graduates. Find the probability thatmeanof this sample is more than 179000 dollars.

P(Sample Mean> 179000) =

1. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.3 years, and standard deviation of 1.2 years.

If you randomly purchase one item, what is the probability it will last longer than 1 years?

Round your answer to at least 3 decimal places.

2.

A particular fruit's weights are normally distributed, with a mean of 381 grams and a standard deviation of 20 grams.

If you pick one fruit at random, what is the probability that it will weigh between 432 grams and 438 grams?

Round answer to at least 3 decimal places.

3. A particular fruit's weights are normally distributed, with a mean of 653 grams and a standard deviation of 37 grams.

The heaviest 18% of fruits weigh more than how many grams?

Give your answer to the nearest 0.1 gram

9. The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 119 millimeters of mercury (mmHg) and standard deviation of 22.

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher. Stage 1 high BP is specified as systolic BP between 140 and 160.

1. What is the probability that an adult in the USA has stage 2 high blood pressure?
2. What is the probability that an adult in the USA has stage 1 high blood pressure?
3. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP?
4. mmHg
5. What is the systolic blood pressure that cuts off the top 2.5% of adults in the USA?
6. mmHg