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Find the area of the shaded region. The graph to the right depicts IQ scores of?...

Question

Find the area of the shaded region. The graph to the right depicts IQ scores of?...

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.

the shaded area reads 90

Answers

Concepts and reason

Normal distribution:

Normal distribution is a continuous distribution of data that has the bell-shaped curve. The normally distributed random variable x has meanand standard deviation

Also, the standard normal distribution represents a normal curve with mean 0 and standard deviation 1. Thus, the parameters involved in a normal distribution are mean and standard deviation.

Standardized z-score:

The standardized z-score represents the number of standard deviations the data point is away from the mean.

• If the z-score takes positive value when it is above the mean (0).

• If the z-score takes negative value when it is below the mean (0).

Fundamentals

Let X-N(u,0) , then the standard z-score is found using the formula given below:

11-X

Where X denotes the individual raw score, denotes the population mean and denotes the population standard deviation.

Instructions to build the shaded area and p-value is given below:

1.In EXCEL, Select Add-Ins > MegaStat > Probability.

2.Choose Continuous probability distributions.

3.Select Normal distribution and select calculate P given z and enter z as ____.

4.Enter mean as ____ and standard deviation as ___.

5.Click Ok.

The z-score for the shaded area X equals 90 is calculated as follows:

Let X denotes the IQ scores of adults which follows normal distribution with mean 100 and the standard deviation 15. That is u=100,0 =15 .

The required z-score is,

2=x-и о 90-100 15 -10 15 =-0.67

The probability area for the shaded region is obtained as follows:

Instructions to build the shaded area and p-value is given below:

1.In EXCEL, Select Add-Ins > MegaStat > Probability.

2.Choose Continuous probability distributions.

3.Select Normal distribution and select calculate P given z and enter z as -0.67.

4.Enter mean as 0 and standard deviation as 1.

5.Click Ok.

Follow the above instructions to get the shaded are and p-value in the output as shown below:

Normal distribution P(lower) P(upper) .2514 7486 z -0.67

From the EXCEL output the p-value for the dark grey region is shaded area until 90 is 0.2514.

Ans:

Thus, the probability of shaded area reads until 90 is 0.2514


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