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Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0 and σ=15.0. A random sample of 59 people is taken. Step 1 of 2 : What is the probability of a random person on the street having an IQ score of less than 98 ? Round your answer to 4 decimal places, if necessary.

Respuesta :

Using the normal distribution, it is found that there is a 0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, the mean and the standard deviation are, respectively, given by [tex]\mu = 100[/tex] and [tex]\sigma = 15[/tex].

The probability of a random person on the street having an IQ score of less than 98 is the p-value of Z when X = 98, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{98 - 100}{15}[/tex]

[tex]Z = -0.13[/tex]

[tex]Z = -0.13[/tex] has a p-value of 0.4483.

0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.

More can be learned about the normal distribution at https://brainly.com/question/24663213

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