Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

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Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

math Statistics-And-Probability

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Answer 1

Answer #1

Concepts and reason

The concept used in this situation is normal distribution.

Normal distribution is a continuous distribution and important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distribution are not known.

The standard normal distribution is a type of normal distribution with mean equal to zero and standard deviation is equal to 1.

Fundamentals

The formula for the calculating z score is,

The Excel’s formula for the calculating probability value of z score is,

The formula for the calculating the probability of between values is,

From the information, observe that the adults have IQ scores of the adults are normally distributed with mean and standard deviation

Consider X is the random variable that represents the adults has IQ scores.

Calculation of the adult has IQ scores less than 70 is as follows:

The calculation of the adult has IQ score is less than 120 is as follows:

The calculation of the required probability is,

Ans:

The calculated probability value of the adults has an IQ score between 70 and 120 is 0.8860

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Answer 2

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