A botanist measures the heights of 16 seedlings and obtains a mean and standard deviation of 72.5 cm and 4.5 cm, respectively. Find the 95 percent confidence interval for the mean height of seedlings in the population from which the sample was selected.

a. 170.54,7446)
b. 7010, 7490]
c. [70.30.7470
d. [62.91.82.09]
e. [71.90, 73101

c. [70.30, 74.70]

Step-by-step explanation:

Confidence interval is a range of values in which there is a specified probability that the value of a parameter lies within that range.

The confidence interval of a statistical data can be written as.

x+/-zr/√n 1

Given;

Mean gain x = 72.5 cm

Standard deviation r = 4.5 cm

Number of samples n = 16

Confidence interval = 95%

z (at 95% confidence) = 1.96 (from the table)

Substituting the values we have into equation 1;

72.5 +/- 1.96×4.5/√16

72.5 +/- 2.20 cm

[70.30, 74.70]

Therefore, the 95% confidence interval is

[70.30, 74.70] cm

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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