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?

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%

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

27

step-by-step explanation: