State whether the following statements are true of the normal distribution curve:
There are the same number of scores above and below the mean.
The curve is symmetrical.
The fewest scores lie around the mean.
The curve is asymmetrical.
The spread of the normal distribution changes depending on the mean.
A higher mean will result in a skewed curve.
The mean, median and mode all have the same value.
The spread of the normal distribution changes depending on the standard deviation.
State whether the following graphs of data are normally distributed:
State whether the following histograms are normally distributed:
Given a normal distribution, state the percentage of people that lie:
Above the mean.
Below the mean.
Consider the given normal distribution:
State the mean.
State the median.
State the mode.
The mean of a set of scores, denoted by \mu is 51 and the standard deviation, denoted by \sigma is 16. Find the value of the following:
\mu - \sigma
\mu + 2 \sigma
\mu + 3 \sigma
\mu - 2 \sigma
\mu + 0.5 \sigma
\mu - \dfrac{2 \sigma}{3}
A data set has a mean of 80 and a standard deviation of 3. Find the score that is 3 standard deviations above the mean.
The following graph shows the distribution of females’ heights in a population:
If 34\% of females lie between 157\text{ cm} and 163\text{ cm}, find the percentage of females that lie between 163\text{ cm} and 169\text{ cm}.
State the value of 1 standard deviation.
The results from an exam were approximately normally distributed. The mean score was 65, with a standard deviation of 9. The points marked on the horizontal axis are separated by 1 standard deviation:
State the value of x on the graph.
State the value of y on the graph.
Assume the mass of sumo wrestlers is normally distributed, with a mean mass of 158\text{ kg} and a standard deviation of 10\text{ kg}.
State the percentage of wrestler that would weigh more than 158\text{ kg}.
How far below the mean is a sumo wrestler who weighs 148\text{ kg}.
In a male population, the mean height was 175\text{ cm}, with a standard deviation of 7\text{ cm}.
State the height of Bob who is 4 standard deviations above the mean.
State the height of John who is 2 standard deviations below the mean.
A sample of professional basketball players is normally distributed and gives the mean height as 199\text{ cm} with a standard deviation of 10\text{ cm}. State the height of a basketball player who is:
3 standard deviations above the mean
1.5 standard deviations below the mean