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Consider the probability that fewer than 46 out of 134 students will not pass their college placement exams. Assume the probability that a given student will not pass their college placement exam is 98%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
a. Yes
b. No

Sagot :

Answer:

b. No

Step-by-step explanation:

Binomial approximation to the normal:

Binomial distribution has n trials, with p probability.

If

[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], it can be approximated to the normal distribution.

Assume the probability that a given student will not pass their college placement exam is 98%.

This means that [tex]p = 0.98[/tex]

134 students:

This means that [tex]n = 134[/tex]

Necessary conditions:

[tex]np = 134*0.98 = 131.32 \geq 10[/tex]

[tex]n(1-p) = 134*0.02 = 2.68 < 10[/tex]

Since the necessary condition n(1-p) < 10 is not satisfied, the answer is No, given by option b.

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