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25 SAT scores are randomly selected from a population of SAT scores that are normally distributed. The population has a mean of 1518 and standard deviation of 325. What is the probability that the selected 25 scores have a mean between 1550 and 1575?

User Silfheed
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2 Answers

4 votes

Answer:

The correct answer is 0.1227

Explanation:

User RealHowTo
by
6.7k points
5 votes

Answer:

The probability that the selected 25 scores have a mean between 1550 and 1575 will be 0.0316

Explanation:

The population has a Mean
(\mu) of 1518 and standard deviation
(\sigma) of 325.

Formula for finding z-score is:
z=(X-\mu)/(\sigma)

So, the z-scores for the mean between 1550 and 1575 are......


z(X>1550)=(1550-1518)/(325) \approx 0.10


z(X<1575)=(1575-1518)/(325) \approx 0.18

According to the standard normal distribution table:
P(Z<0.10)=0.5398 and
P(Z<0.18)= 0.5714

Now,


P(1550<X<1575)\\ \\ =P(Z<0.18)-P(Z<0.10)\\ \\ =0.5714-0.5398\\ \\ =0.0316

So, the probability that the selected 25 scores have a mean between 1550 and 1575 will be 0.0316

User Rob DiMarco
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6.9k points