Consider the probability that at most 93 out of 127 students will pass their college placement exams. Assume the probability that a given student will pass their college placement exam is 53%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

the answer will be in yes or no format

Yes, the normal curve can be used as an approximation to the binomial probability.

Step-by-step explanation:

Let X = number of students that pass their college placement exam.

The probability that a given student will pass their college placement exam is, P (X) = p = 0.53.

A random sample of n = 127 students is selected.

The random variable X follows a Binomial distribution.

But the sample size is too large.

A Normal approximation to Binomial can be used to approximate the distribution of proportion p.

The conditions to be satisfied are:

Check whether the conditions are satisfied as follows:

Both he conditions are satisfied.

Thus, a normal curve can be used as an approximation to the binomial probability.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

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