State whether the following curves are normally distributed:
Consider the following normal distributions:
State the following values for each distribution:
mean
median
mode
Determine whether the following statements are true for a normal distribution:
The majority of scores from a normal distribution will likely lie around the mean.
The majority of scores from a normal distribution will likely lie away from the mean.
The distribution is symmetric about the mean.
The distribution is asymmetric.
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 mean.
The spread of the normal distribution changes depending on the standard deviation.
Draw normal distribution curves for each of the following values. Mark the horizontal axis with the scores that are 1, 2 and 3 standard deviations from the mean.
mean 306 and standard deviation 32
mean -307 and standard deviation 23
The lengths of female funnel web spiders are approximately normally distributed, with an average length of 225\text{ mm}. The standard deviation is 30 \text{ mm}.
The points marked on the horizontal axis of each distribution below are separated by 1 standard deviation. Determine whether the following shows the distribution of the lengths of female funnel webs:
A biscuit manufacturer claims to use 18.5\text{ g} of sugar in each packet of biscuits.
Due to measurement error, the amount of sugar in each packet of biscuits is approximately normally distributed with mean 18.5\text{ g}.
Determine whether the following shows the possible distribution of sugar in each packet:
The length of the journey from a particular train station into the city is approximately normally distributed and varies with a standard deviation of 4 minutes.
The points marked on the horizontal axis for each distribution below are separated by 1 standard deviation. Determine whether the following shows the possible distribution of journey times into the city:
The pH level of tap water is approximately normally distributed with mean 6.77 and standard deviation of 0.4.
Draw the distribution curve pH levels of tap water.
The heights of trees in a plant nursery are approximately normally distributed with an average height of 177.3\text{ cm}.
What is the median height of the trees in centimeters?
The height of male Australians is approximately normally distributed with an average height of 175.6\text{ cm}.
What is the median height of male Australians in centimeters?
Each year, a charity holds an event in which teams compete to raise funds. The amount of money a team raises is approximately normally distributed. Calculate the average amount raised by a team, if the median amount is:
\$1590
\$1220
The weight of avocados at a grocery store is approximately normally distributed. The average weight is 157\text{ g}. The points marked on the horizontal axis are separated by 1 standard deviation.
What is the standard deviation of the weight of avocados in grams?
What is the value of x on the graph?
What is the value of y on the graph?
The results from an exam were approximately normally distributed. The mean score was 44, with a standard deviation of 6. The points marked on the horizontal axis are separated by 1 standard deviation.
What is the value of x on the graph?
What is the value of y on the graph?
