Statistics and Probability Answers

It has been observed that in Fundamental Statistics course, a students receves on average of 45 marks with a standard deviation of 12 marks out of 60. If the marks obtained students normally distributed Then • Find the probability that a student will score the marks between 24 and 54 Interpret your answer if there are 200 students in the class. How many students we can expect to score marks between 24 to 54

Question 4. An importer of electronic goods is considering packaging a new, easy-to-read instruction booklet with DVD players. It wants to package this booklet only if it helps customers more than the current booklet. Previous tests found that only 30% of customers were able to program their DVD player. An experiment with the new booklet found that 16 out of 60 customers were able to program their DVD player.

(a) State the null and alternative hypotheses.

(b) Describe Type I and Type II errors in this context.

(c) Find the p-value of the test. Do the data supply enough evidence to reject the null hypothesis if alpha = 0.05?

Question 3. A sample of 150 calls to a customer helpline during one week found that callers were kept waiting on average for 16 minutes with s = 8.

(a) Find the margin of error for this result if we use a 95% confidence interval for the length of time all customers during this period are kept waiting.

(b) Interpret for management the margin of error.

(c) If we only need to be 90% confident, does the confidence interval become wider or narrower?

(d) Find the 90% confidence interval.

Question 2. A news report summarizes a poll of voters and then adds that the margin of error is plus or minus 4%. Explain what that means.

Question 1. Which is shorter, a 95% z-interval for the mean or a 95% t-interval for the mean? Is one of these always shorter, or does the outcome depend on the sample?

We wish to train a machine learning algorithm on an array of floating-point numbers in the

interval [0.0, 1.0). The data is horribly unbalanced (not evenly distributed) and we wish to

filter the dataset to obtain a subset containing an equal number of values from each

interval

[0, 0.2), [0.2, 0.4), ... [0.8, 1.0), throwing away as little data as possible.

Write a program which reads comma-separated floating-point numbers in a single line from

standard input and prints the filtered data to standard output in the same format

Note: Solve this in linear time, if possible. Priority will be given to those who solve in linear

time.

Explanation Example

Input: 0.11,0.12,0.13,0.23,0.34,0.35,0.47,0.59,0.77,0.83,0.85,0.91,0.95

On classifying the above input data from example 4, Subset in each interval will look as below:

Since the interval [0.6 - 0.8) has the minimum subset of size 1. We choose 1 element from

the rest of the intervals.

Output: 0.11,0.23,0.47,0.77,0.83

*if the interval [0.6 - 0.8) had more than 3 elements then we would choose 2 elements from all

subset, since the interval with minimum subset, would be [0.4 - 0.6) and of size 2.

Interval Data

[0 - 0.2) 0.11,0.12,0.13

[0.2 - 0.4) 0.23,0.34,0.35

[0.4 - 0.6) 0.47,0.59

[0.6 - 0.8) 0.77

[0.8 - 1.0) 0.83,0.85,0.91,0.95

Sample Examples:

Example 1

Input: 0.1,0.3,0.5,0.7,0.9

Output: 0.1,0.3,0.5,0.7,0.9

Example 2

Input: 0.1,0.3,0.5,0.7,0.9,0.5

Output: 0.1,0.3,0.5,0.7,0.9

Example 3

Input: 0.15,0.12,0.35,0.38,0.55,0.56,0.57,0.75,0.77,0.9,0.94

Output: 0.15,0.12,0.35,0.38,0.55,0.56,0.75,0.77,0.9,0.94

study was conducted to find whether there is any relationship between the weight and blood pressure of an individual. The following set of data was arrived at from a clinical study. The first column represents the serial number and the second and third columns represent the weight and blood pressure of each patient. 

Weight (x)

65

82

71

73

63

72

71

77

71

77

Blood Pressure (y)(y)

 136

145

123

132

175

165

152

158

117

129

Find the coefficient of correlation for this set of data. 

Students in a statistics class weighed 30 bags of regular size M&M’s and found that the average weight of

the 30 bags excluding the wrapper was 1.75 ounces. The net weight printed on the wrapper is 1.69 ounces.

Population:

Sample:

Parameter:

Statistic:

The number of defective units selected when five units are chosen at random from a batch of ten flash drives which contains four detective items

the probability of a particular type of genetic code in human species is 9/25 in a random sampling of a human species what is the probability that at least 6 has that particular type of genetic code