There are two main categories of food - conventional and

Question

1. A grocery store carries the following items. There are two main categories of food - conventional and organic ingredients - and four food groups. The data are shown in the following table.

	Food Groups
Food Categories	Grains	Fruits	Vegetables	Meat	Total
Conventional	133	76	36	77	322
Organic	42	49	264	138	493
Total	175	125	300	215	815

If all of the organic items were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select an organic fruit into your grocery basket? First compute for yourself the row (i.e., n₁₊, n₂₊), column (i.e., n₊₁, n₊₂, n₊₃, n₊₄), and overall (i.e., n₊₊) totals, to aid in answering the question.

2. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 53.88 ng/mL with a standard deviation of 4.866 ng/mL. Assuming the true distribution of blood vitamin D levels follows a normal distribution, if you randomly select a landscaper in the US, what is the probability that his/her vitamin D level will be between 48.13 and 60.03 ng/mL?

3. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 53.04 ng/mL with a standard deviation of 4.308 ng/mL. Assuming the true distribution of blood vitamin D levels follows a normal distribution, what is the upper value of the region for which approximately 99.9% of the data are located within the distribution? Recall the 68-95-99.9% observation discussed in the "Normal Distribution" section of the textbook that is helpful in answering the question.

4. Suppose at random 44% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=19. What is the probability that 16 or less, or more than 17 children become sick?

5. Suppose at random 35% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=47. What is the probability that less than 25, or 36 or more children become sick?

6. A grocery store carries the following items. There are two main categories of food - conventional and organic ingredients - and four food groups. The data are shown in the following table.

	Food Groups
Food Categories	Grains	Fruits	Vegetables	Meat	Total
Conventional	2	15	235	202	454
Organic	173	110	65	13	361
Total	175	125	300	215	815

If all of the items were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select a conventional grain or fruit in your grocery basket? First compute for yourself the row (i.e., n₁₊, n₂₊), column (i.e., n₊₁, n₊₂, n₊₃, n₊₄), and overall (i.e., n₊₊) totals, to aid in answering the question.

7. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 37.58 ng/mL with a standard deviation of 5.474 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, if you randomly select a landscaper in the US, what is the probability that his/her vitamin D level will be 41.04 ng/mL or less?

8. A grocery store carries the following items. There are two main categories of food - conventional and organic ingredients - and four food groups. The data are shown in the following table.

	Food Groups
Food Categories	Grains	Fruits	Vegetables	Meat	Total
Conventional	119	35	202	48	404
Organic	56	90	98	167	411
Total	175	125	300	215	815

If all of the grains, fruits, and vegetables were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select a grain, fruit, or vegetable that is conventional into your grocery basket? First compute for yourself the row (i.e., n₁₊, n₂₊), column (i.e., n₊₁, n₊₂, n₊₃, n₊₄), and overall (i.e., n₊₊) totals, to aid in answering the question.

9. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 36.15 ng/mL with a standard deviation of 4.737 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, if you randomly select a landscaper in the US, what is the probability that his/her vitamin D level will be 49.54 ng/mL or less?

10. 48% of mosquitos caught at random in any given field study carry malaria. If you conduct a study and capture 34 mosquitos, how many mosquitos infected with malaria would you expect to have in your mosquito-catching Mason jar out of all 34 mosquitos buzzing around? Round up to the nearest whole number if your calculation results in a number with decimal point values. For example, 0.2 rounds up to 1 and 74.25 rounds up to 75.

11. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 37.64 ng/mL with a standard deviation of 5.107 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, if you randomly select a landscaper in the US, what is the likelihood that his/her vitamin D level will be 32.74 ng/mL or more?

12. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 47.07 ng/mL with a standard deviation of 5.162 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, what is the 66-th percentile? Recall that the statistic, "percentile", is defined to be the value below which a given percentage of observations are located within the distribution. In other words, for this question find the vitamin D value for which 66% of the observations within the distribution are located to the left of this value.

13. Suppose at random 30% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=22. What is the probability that between more than 0 and 15 or less children become sick?

14. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 39.72 ng/mL with a standard deviation of 4.891 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, if you randomly select a landscaper in the US, what is the likelihood that his/her vitamin D level will be between 29.29 and 38.24 ng/mL?

15. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 33.4 ng/mL with a standard deviation of 5.282 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, what is the lower value of the region for which approximately 95% of the data are located within the distribution? Recall the 68-95-99.9% observation discussed in the "Normal Distribution" section of the textbook that is helpful in answering the question.

16. A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 32.02 ng/mL with a standard deviation of 5.231 ng/mL. Assuming the true distribution of blood vitamin D levels follows a normal distribution, if you randomly select a landscaper in the US, what is the probability that his/her vitamin D level will be 31.33 ng/mL or more?

17. A grocery store carries the following items. There are two main categories of food - conventional and organic ingredients - and four food groups. The data are shown in the following table.

	Food Groups
Food Categories	Grains	Fruits	Vegetables	Meat	Total
Conventional	91	107	281	64	543
Organic	84	18	19	151	272
Total	175	125	300	215	815

If all of the items were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select a fruit, vegetable, or meat in your grocery basket, regardless if it's conventional or organic? First compute for yourself the row (i.e., n₁₊, n₂₊), column (i.e., n₊₁, n₊₂, n₊₃, n₊₄), and overall (i.e., n₊₊) totals, to aid in answering the question.