Question

The grades on a short quiz in biology were 0,1,2,4...10 points , depending upon the number of correct answer out of question. the mean grades was 6.7 with standard deviation of 1.2 . assuming the grades to be normally distributed ,determine ,(1) the % of students scoring 60 points , (2) the maximum grades of the lowest 10% of the class​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

1. Percentage of students scoring less than 6 points = 27.98%

2. Maximum score of the lowest 10% of the class is 5.162.

Given that,

A brief biology quiz awarded grades based on how many of the 10 questions had the correct answer (0, 1, 2,.....10 points). If the grades were regularly distributed, the mean was 6.7 and the standard deviation was 1.2.

We have to find calculate the percentage of pupils scoring a 6 and the worst 10% of the class's average grades​.

We know that,

Mean score of the quiz = 6.7

Standard deviation of the score of the quiz = 1.2

1. P (S < 6)

Z = $\frac{(x -\mu)}{\sigma}$$\frac{(x -\mu)}{\sigma}$ = $\frac{(6-6.7)}{1.2}$ = -0.5833

P (Z < -0.5833) = 0.2798

Therefore, Percentage of students scoring less than 6 points = 27.98%

2. In this case, the p-value = 0.1

Z-value corresponding to probability 0.1 on the left side of the curve is -1.28155

Z = $\frac{(x -\mu)}{\sigma}$ = $\frac{(x-6.7)}{1.2}$ = -1.28155

x = 6.7 + (-1.28155 × 1.2) = 5.162

Therefore, maximum score of the lowest 10% of the class is 5.162.

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