32. Use Structure Write an inequality that represents the graph.

teacher gives 5 students a multiple choice test, in which each problem is worth 1 point and there is no penalty with negative po

mamaluj [8]

The mean is the average value of a given set of numbers, and the median is the number in the middle of a set of numbers arranged in increasing order

The correct values as response to the questions are;

The minimum possible top score is 21

The maximum possible top score is 32

The minimum of the possible standard deviation is approximately 1.26

The maximum of the possible standard deviation is approximately 11.7

The reason the above values are correct are as follows:

The given parameters are;

The number of students that take the test, n = 5

The amount of points for each problem = 1 point

The median score = 9

The mean Score = 10

Required:

The minimum possible score;

The maximum possible top score

The minimum of the possible standard deviations

The maximum of the possible standard deviations

Solution:

Given that there is a score (the median) which is 9, we have;

The scores obtainable in the test is Scores ≥ 9

Therefore, for a score of 10, we have;

The minimum total points obtainable = Mean × Number of students

Therefore;

Total minimum total points obtainable by the 5 students = 5 × 10 = 50

The minimum possible top score

By arrangement, with the median at the middle, the minimum possible top score is given as follows;

0, 0, 9, 20, 21

Therefore, the minimum possible top score is 21

The maximum possible top score

The maximum possible top score is similarly given by arrangement of the numbers as follows'

0, 0, 9, 9, 32

The maximum possible top score is 32

The minimum standard deviation

By arrangement and selection, the minimum standard deviation is given as follows;

The minimum of the possible standard deviations of (9, 9, 9, 11, 12) ≈ 1.26

The maximum of the possible standard deviation

The maximum of the possible standard deviation is given as follows;

The maximum of the possible standard deviation of (0, 0, 9, 9, 32) ≈ 11.7

Learn more about mean and median here:

brainly.com/question/17012793

8 0

3 years ago

A corporation has 11 manufacturing plants. Of these, seven are domestic and four are outside the United States. Each year a perf

nikdorinn [45]

Answer:

The probability that a performance evaluation will include at least one plant outside the United States is 0.836.

Step-by-step explanation:

Total plants = 11

Domestic plants = 7

Outside the US plants = 4

Suppose X is the number of plants outside the US which are selected for the performance evaluation. We need to compute the probability that at least 1 out of the 4 plants selected are outside the United States i.e. P(X≥1). To compute this, we will use the binomial distribution formula:

P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = total no. of trials

x = no. of successful trials

p = probability of success

q = probability of failure

Here we have n=4, p=4/11 and q=7/11

P(X≥1) = 1 - P(X<1)

= 1 - P(X=0)

= 1 - ⁴C₀ * (4/11)⁰ * (7/11)⁴⁻⁰

= 1 - 0.16399

P(X≥1) = 0.836

The probability that a performance evaluation will include at least one plant outside the United States is 0.836.