Question

Determine whether the BEST, most common interpretation of the given statement is:

     TRUE - Select 1

     FALSE - Select 2

Question 1 options:

12 As the STANDARD DEVIATION increases for a NORMAL distribution, the values become less concentrated around the mean. 12 The MODE of a standard normal distribution is one. 12 A SYMMETRIC histogram, implies the plotted variable is NORMALLY distributed. 12 The sample proportion PHAT from a sample of size n estimating a population proportion p will have an approximate normal distribution with MEAN equal to np, assuming the normality conditions hold. 12 A NORMAL distribution will have an approximately SYMMETRIC histogram. 12 For a PROBABILITY DENSITY FUNCTION, the area under the entire curve for a continuous variable is one. 12 The CENTRAL LIMIT THEOREM says that for large samples the sample mean will have an approximate NORMAL distribution for data coming from any distribution. 12 The EMPIRICAL RULE gives approximate probabilities for areas within +/- 1,2 or 3 standard deviations of the mean for any normal distribution. 12 A Z-SCORE can be interpreted for a value as the value's number of standard deviation above or below the mean. 12 For a CONTINUOUS variable X, the probability X exactly equals any individual point is zero.

1. TRUE 2. FALSE

Question 2 (20 points)

Answer 1

12) As the STANDARD DEVIATION increases for a NORMAL distribution, the values become less concentrated around the mean- We know that standard deviation increases as the deviation (distance) of a point increases from mean,

Hence this is TRUE.

12) The MODE of a standard normal distribution is one - Mode is the most repeated observation in the data, in standard normal distribution we get mean 0 and standard deviation 1, that is most observations are 0.

Hence this is FALSE.

12) A SYMMETRIC histogram, implies the plotted variable is NORMALLY distributed.

A Normal distribution has bell shaped curve. Hence it shows symmetric shape.

Hence This is TRUE.

12) The sample proportion PHAT from a sample of size n estimating a population proportion p will have an approximate normal distribution with MEAN equal to np, assuming the normality conditions hold.

For sample proportion p^= x / n where n is sample size, follows Normal distribution with mean= n*p and standard deviation =sqrt(n*p*(1-p))

12) A NORMAL distribution will have an approximately SYMMETRIC histogram.

Normal distribution shows bell shaped curve, hence this is TRUE.

12) For a PROBABILITY DENSITY FUNCTION, the area under the entire curve for a continuous variable is one.

The total area under the curve for a continuous variable is one, hence this is TRUE.

12) The CENTRAL LIMIT THEOREM says that for large samples the sample mean will have an approximate NORMAL distribution for data coming from any distribution.

As the sample size increases the distribution of data follows NORMAL. Hence this is TRUE.

12) The EMPIRICAL RULE gives approximate probabilities for areas within +/- 1,2 or 3 standard deviations of the mean for any normal distribution.

By empirical rule 68% are will fall within 1 Standard deviation. 95% are will fall within 2 Standard deviation. and 99.7% are will fall within Standard deviation. Hence this is TRUE.

12)A Z-SCORE can be interpreted for a value as the value's number of standard deviation above or below the mean.

Z score shows the number of Standard deviation a value is far from mean. Hence this is TRUE.

12) For a CONTINUOUS variable X, the probability X exactly equals any individual point is zero.

For a continuous variable X, we can compute the less than probability, for exact point we get the probability as 0.

Hence this is TRUE.

Hope this will help you. Thank you :)