1.We will investigate the Short Term Memory scores for the subjects in the data set (variable STM); call this variable X. Assume the population values of STM are Normally distributed with mean 30 and standard deviation 20.

a)(2 points) Find the probability an individual, selected at random, has a STM less than 35. Show your work. The correct probability statement is required to get full credit. Write final answer to 4 decimal places.

b)(3 points) Label the axis in terms of STM, including the values for the individual in part (a) and the population mean.Shade the area representing the probability in part (a) and indicate its value.

c)(3 points) Label the axis in terms of z, including the values for the individual in part (a) and the population mean.Shade the area representing the probability in part (a) and indicate its value.

d)(2 points) What is the probability an individual selected at random will have a STM greater than 45 pounds? Show your work. The correct probability statement is required to get full credit. Round final answer to 4 decimal places.

e) (3 points) What STM value is the cut-off value for the top 60% of STM?Show your work. You must start off by writing down the correct probability statement. Round final answer to 1 decimal place.

f) (2 points) Based on problem (e) above, label the axis in terms of STM, including the values for the cut-off score for the highest 60% and the population mean.Shade the area representing the probability in question and indicate its value.