The cholesterol levels in healthy individuals are approximately normally distributed. For males under 21 in a population, the average cholesterol level is162mg/dlwith a standard deviation of12mg/dl.

1. Identifyand for this question.
2. If a male under 21 is selected at random, find the probability that his cholesterol level is above191mg/dl.

a)Find the Z-score (show your work using thenumericalvalues in the formula and round the z-score totwodecimal places) for191:

b. Sketch the corresponding region to the statement with the Z-score. Select from the dropdown menu to shade to the left, to the right, between or left and right of the Z-score(s); and then shade the corresponding region. The arrow can only drag to the Z-score that is rounded toonedecimal place (these values correspond to the tick marks on the horizontal axis).

c. Find the left-cumulative area (keep4decimal places) corresponding to the Z-score:

d. Find the left-cumulative area (keep4decimal places) corresponding to the Z-score: p(x>191)

If a male under 21 is selected at random, find the probability that his cholesterol level is between142mg/dland152mg/dl.

a. Find Z₁-score (show your work using thenumericalvalues in the formula and round the z-score totwodecimal places) for142:

b. Find Z₂-score (show your work using thenumericalvalues in the formula and round the z-score totwodecimal places) for152

c. Sketch the corresponding region to the statement with the Z-scores. Select from the dropdown menu to shade to the left, to the right, between or left and right of the Z-score(s); and then shade the corresponding region. The arrow can only drag to the Z-scores that are rounded toonedecimal place (these values correspond to the tick marks on the horizontal axis).

d.Find the left-cumulative area 1 (keep4decimal places) corresponding to the Z₁-score: e. Find the left-cumulative area 2 (keep4decimal places) corresponding to the Z₂-score: f. Answer(show your work and keep4decimal places):

P(142

Find the cut off cholesterol level to be in the bottom 10% of the distribution.

a)The bottom 10 % of the distribution indicates

• both tailed areas
• right-tailed area
• left-tailed area
• center area

b. Find the closest left cumulative area (keep4decimal places) in the table: c)Read the Z-score corresponding to the closest area in question b: d)Show a mathematical expression with thenumericalvalues, without evaluating any part of the expression to find the final answer (use * for multiply): e)Write the answer (do not round) including the unit shown in this question:

1. If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a spade or diamond?
2. If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a Ace or 3?
3. If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a diamond or 3?