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DaniilM [7]
3 years ago
12

A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.

Using the eight‐part symmetry of the area under a normal curve, what is the probability that a randomly chosen exam score is less than 200 or greater than 800?
The probability is__?
Mathematics
1 answer:
yawa3891 [41]3 years ago
6 0

Answer:

The probability is  0.003

Step-by-step explanation:

We know that the average \mu is:

\mu=500

The standard deviation \sigma is:

\sigma=100

The Z-score is:

Z=\frac{x-\mu}{\sigma}

We seek to find

P(x800)

For P(x>800) The Z-score is:

Z=\frac{x-\mu}{\sigma}

Z=\frac{800-500}{100}

Z=3

The score of Z = 3 means that 800 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

P(x>800)=0.15\%

For P(x<200) The Z-score is:

Z=\frac{x-\mu}{\sigma}

Z=\frac{200-500}{100}

Z=-3

The score of Z = -3 means that 200 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

P(x

Therefore

P(x800)=P(x800)

P(x800)=0.0015 + 0.0015

P(x800)=0.003

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