In standard normal distribution of a normal curve has a mean of__________ and a standard deviation of____________.

Correct option is D

A standard normal distribution is a special case of the normal distribution, where:
· The mean (μ) is 0.
· The standard deviation (σ) is 1.
This distribution is often represented by the variable ZZZ, which measures the number of standard deviations a data point is from the mean.
Key Characteristics of the Standard Normal Distribution: 1. Symmetry:
· The curve is symmetric about the mean (μ=0\mu = 0μ=0).
2. Standardized Scale:
· The ZZZ-score represents data in terms of standard deviations. For example:
· Z=1Z = 1Z=1: Data point is 1 standard deviation above the mean.
· Z=−1Z = -1Z=−1: Data point is 1 standard deviation below the mean.
3. Total Area Under the Curve:
· Equals 1, representing the entire probability distribution.
Explanation of Other Options: · (a) 1 and 0: Incorrect, as the standard normal distribution does not have a mean of 1.
· (b) 0 and 0: Incorrect, as the standard deviation cannot be 0 in a normal distribution.
· (c) 1 and 1: Incorrect, as the standard normal distribution has a mean of 0, not 1.
Correct Answer: (d) 0 and 1 Information Booster 1. Applications of Standard Normal Distribution:
· Used in hypothesis testing and z-tests.
· Helps in converting raw scores into standardized ZZZ-scores.
2. Properties of Normal Curve:
· Bell-shaped and symmetric about the mean.
· Approximately 68% of data lies within 1 standard deviation, 95% within 2, and 99.7% within 3.
3. Formula for ZZZ-Score:
Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ​
Where XXX is the raw score, μ\muμ is the mean, and σ\sigmaσ is the standard deviation.