Hints:  Consider the diagram below and notice that there is a left tail and a right tail that must make a combined 0.05 area.

  • Use the fact that the sampling distribution (X distribution) has mean m and standard deviation s divided by the square root of n.

  • To find a probability that involves the mean use normalcdf(a,b,mu,sigma/root(n))

    • a is the lower bound.  Use -99999 if there is no lower bound (negative infinity).

    • b is the upper bound.  Use 99999 if there is no upper bound (infinity).

    • m is the population mean

    • s is the population standard deviation

    • n is the sample size.

  • To find a percentile or quartile:  Q1 = 25th percentile and Q3 = 75th percentile, use invNorm(x,mu,sigma/root(n)).  Other wordings are find the value such that 30% (x = 0.3) of the data lies below the value.  If you want to find the value such that a given percentage lies above that value, use the rule of complements.  For example if 10% lies above, then 90% lies below.

  • Use the fact that the distribution of a sum of values has mean nm and standard deviation s times the square root of n.

  • To find a probability that involves the sum use normalcdf(a,b,n*mu,sigma*root(n))

  • To find the Inter-Quartile-Range (IQR), find the first quartile (25th  percentile) and the third quartile (75th percentile) and subtract.