Question

1. A student has the following assignment grades: 85, 92, 72, 69, 74, 96, 83, 76, 72, 97. Find the mean, mode, and the five-number summary. Round to one decimal

2. Find the mean and the standard deviation of the following quiz scores:
   21, 20, 23, 15, 16. Round to one decimal.

3. 15,000 students take a national test. The results are normally distributed with a mean of 400 and a standard deviation of 120. Approximately how many students scored between 400 and 520 on the test? (Do not round.

4. It is known that under ordinary circumstances, 18% of people will not contract a certain disease. Consider the situation where test groups of 600 were selected and the percentages that did not contract the disease were recorded. According to the Central Limit Theorem, the data collected are approximately normally distributed.

   Ø Find the mean and standard deviation of this normal distribution. Round to one decimal. [15 points]

   Ø What is the percentage of test groups of 600 people in which 16% or less do no contract the disease?

5. A polling organization conducts a poll by making a random survey of 1600 people. Estimate the margin of error at a confidence level of 95%. Round to one decimal.

6. A polling organization conducts a poll by making a random survey and is willing to accept a margin of error of 4% at a confidence level of 95%. What should the sample size be? Next, the poll reported a 62% approval. What is the confidence interval for this poll at a confidence level of 95%?

7. Suppose that for a certain illness, the probability is 40% that a given patient will improve without treatment. Then the probability that at least n out of 20 patients will improve without treatment is given in the following table: We gave an experimental drug to 20 patients who have the illness and 16 patients showed improvement. What is the p-value? (Do not round.)   Suppose we count the test significant if the p-value is 0.05 or less. How many patients must show improvement in order to make the test statistically significant?

   n	12	13	14	15	16
   Probability at least n improve	0.1538	0.0675	0.0505	0.013	0.0054

Answer 1

Que.1

In order to solve this question I used R software.

R codes and output:

> x=c(85, 92, 72, 69, 74, 96, 83, 76, 72, 97)
> table(x)
x
69 72 74 76 83 85 92 96 97
1 2 1 1 1 1 1 1 1
> summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
69.00 72.50 79.50 81.60 90.25 97.00

Mean = 81.60

Mode = 72

Five number summary:

Min	Q1	Median	Q3	Max
69	72.5	79.5	90.3	97

Que.2

R codes and output:

> y=c(21, 20, 23, 15, 16)
> mean(y)
[1] 19
> sd(y)
[1] 3.391165

Mean = 19

Standard deviation = 3.4

Que.3

Probability that student who scored between 400 to 520 is 0.3413

Hence number of students out of 15000 who scored between 400 to 520 =  15000 * 0.3413 = 5119.5

Approximately 5120 students out of 15000, have score between 400 to 520