Understanding Standard Normal Distribution

The video tutorial explains how to find a Z-score (C) for a standard normal distribution where the probability of Z being less than C is 0.614. It highlights that since the probability is greater than 50%, the Z-score will be positive. The tutorial guides viewers on using a cumulative Z-score table to find the closest value to 0.614, which is 0.6141, corresponding to a Z-score of approximately 0.29. This Z-score indicates that the probability of a randomly selected data value having a Z-score less than 0.29 is about 61.4%.

What is the probability that a Z-score is less than C in a standard normal distribution?

• 0.29

• 0.75

• 0.614

• 0.5

Why is the Z-score positive when the probability is greater than 50%?

• Because the data value is negative

• Because the data value is at the mean

• Because the data value is above the mean

• Because the data value is below the mean

What does a Z-score of zero indicate in a standard normal distribution?

• The data value is at the mean

• The data value is negative

• The data value is above the mean

• The data value is below the mean

How do you find the Z-score for a given probability using the cumulative Z-score table?

• By looking for the exact probability value

• By finding the closest probability value

• By calculating the mean

• By using the standard deviation

What is the Z-score corresponding to a probability of 0.614?

• 0.75

• 0.5

• 0.614

• 0.29

What does the area to the left of a Z-score on the standard normal distribution curve represent?

• The standard deviation of the distribution

• The mean of the distribution

• The probability of a Z-score being less than the given value

• The probability of a Z-score being greater than the given value

If a randomly selected data value has a Z-score less than 0.29, what is the probability?

• 0.75

• 0.29

• 0.5

• 0.614