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If the scores of a math test are normally distributed with an average score of 76 and a standard deviation of 5, what percentage of students scored below a 65?

Respuesta :

Answer:

Step-by-step explanation:

Since the scores of the math test are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = math test scores.

µ = mean score

σ = standard deviation

From the information given,

µ = 76

σ = 5

The probability that a student scored below 65 is expressed as

P(x < 65)

For x = 65

z = (65 - 76)/5 = - 2.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.014

The percentage of students that scored below 65 is

0.014 × 100 = 1.4%

The percentage of students who scored below 65 is 1.4%.

Calculation of the percentage of the students scored:

Since  the scores of a math test are normally distributed with an average score of 76 and a standard deviation of 5,

So here we find the z score i.e.

z = [tex](65 - 76)\div 5[/tex]

= - 2.2

Now look at the table so here the percentage should be 1.4%

hence, The percentage of students who scored below 65 is 1.4%.

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