Answers
Normal distribution:
Normal distribution is a continuous distribution of data that has the bell-shaped curve. The normally distributed random variable x has mean
and 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).
Let 
, then the standard z-score is found using the formula given below:
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 
.
The required z-score is,
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:
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
.