Cards In This Deck

• $$\begin{gathered} \text{True or False? } \\ \text{For a continuous normal random variable, the probability }P(X\le 50)\text{ is greater than }P(X<50)\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }P(X\le 50)=P(X<50) \end{gathered}$$
• $\text{For a normal distribution curve, what is the total area under the bell curve?}$
  $Area=1$
• $$\begin{gathered} \text{At which specific points on the }x\text{-axis do the points of inflection occur for the normal distribution }N( \\ \mu , \\ {\sigma }^2)\text{?} \end{gathered}$$
  $$\begin{gathered} \text{At }x= \\ \mu - \\ \sigma \text{ and }x= \\ \mu + \\ \sigma \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{If }X\sim N(100,25)\text{, then the standard deviation is 25.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{Correct reasoning: The Normal notation is }N( \\ \mu , \\ {\sigma }^2)\text{. The second number is the Variance.} \\ \text{Standard Deviation } \\ \sigma =\sqrt{25}=5\text{.} \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{If a random variable is defined as }X\sim N(20,16)\text{, then the standard deviation } \\ \sigma =16\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: } \\ \sigma =4 \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{If }X\sim N(100,25)\text{, then }P(X<90)\text{ corresponds to a }Z\text{-score of }\frac{90-100}{25}=-0.4\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }Z=\frac{90-100}{\sqrt{25}}=\frac{-10}{5}=-2 \end{gathered}$$
• $$\begin{gathered} \text{What is the formula to standardize a value }X\text{ from a normal distribution }N( \\ \mu , \\ {\sigma }^2)\text{ to the standard normal distribution }Z\text{?} \end{gathered}$$
  $$\begin{gathered} Z=\frac{X- \\ \mu }{ \\ \sigma } \end{gathered}$$
• $$\begin{gathered} \text{How do you solve a Normal Distribution problem where you need to find probabilities for }X\sim N( \\ \mu , \\ {\sigma }^2)\text{?} \end{gathered}$$
  $$\begin{gathered} \text{Standardize the variable to }Z\text{ using:} \\ Z=\frac{X- \\ \mu }{ \\ \sigma } \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{If }P(Z<a)=0.25\text{, then the value of }a\text{ must be positive.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }a\text{ must be negative.} \end{gathered}$$
• $\text{You need to find a }z\text{-value such that }P(Z>z)=0.05\text{. Which table is most efficient to check first?}$
  $\text{The Percentage Points table.}$
• $$\begin{gathered} \text{True or False? } \\ \text{When calculating }P(a<Z<b)\text{, the correct method is }\Phi (a)-\Phi (b)\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }\Phi (b)-\Phi (a) \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{To find }P(Z>-1.25)\text{, you should calculate }1-P(Z<1.25)\text{.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: }P(Z>-1.25)=P(Z<1.25) \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{If you need to find }z\text{ such that }P(Z>z)=0.8\text{, you can look up }p=0.8\text{ in the Percentage Points table.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Answer: The Percentage Points table usually only lists small probabilities (}p<0.5\text{).} \end{gathered}$$
• $$\begin{gathered} \text{You are given }P(X<20)=0.15\text{ and }P(X>40)=0.05\text{ and asked to find the mean } \\ \mu \text{ and standard deviation } \\ \sigma \text{. How do you start?} \end{gathered}$$
  $\text{Form two simultaneous equations using the standardization formula.}$