Normal Probability Density

What is the normal probability density often compared to in terms of its prevalence in nature?

• Cosine wave

• Sine wave

• Tangent wave

• Exponential function

In a discrete probability distribution, what must the sum of all probabilities equal?

• Zero

• One

• Infinity

• The number of outcomes

What is a key difference between discrete and continuous probability distributions?

• Discrete distributions can take any value, continuous cannot

• Continuous distributions can take any value, discrete cannot

• Discrete distributions are always normally distributed

• Continuous distributions are always normally distributed

What is the mean and standard deviation of the standard normal distribution?

• Mean of 0, standard deviation of 0

• Mean of 1, standard deviation of 1

• Mean of 0, standard deviation of 1

• Mean of 1, standard deviation of 0

When using standard normal distribution tables, what does the value represent?

• The probability of the mean

• The cumulative probability from that point to the right

• The cumulative probability from that point to the left

• The probability at that exact point

What is the main reason some tables do not include negative Z-values?

• Negative Z-values are not relevant for most applications.

• Negative Z-values are not used in statistics.

• Negative Z-values can be derived from positive Z-values due to symmetry.

• Negative Z-values are too complex to calculate.

In a normal distribution with a mean of 100 and a standard deviation of 15, what is the probability of a value being less than 115?

• 0.8413

• 0.1587

• 0.5000

• 0.3413

If a standardized test has a mean score of 998 and a standard deviation of 202, what percentage of students score below 1100?

• 50.00%

• 29.12%

• 15.87%

• 70.88%

How do you determine the minimum score required to be in the top 40% of a normally distributed test?

• Use the mean and subtract the standard deviation.

• Find the Z-score for 0.4 and calculate the corresponding test score.

• Use the mean and add the standard deviation.

• Find the Z-score for 0.6 and calculate the corresponding test score.

For a product with a mean lifespan of 8.2 years and a standard deviation of 1.1 years, how long should a warranty be to cover only 1% of failures?

• 8.2 years

• 7.1 years

• 5.67 years

• 6.5 years