Here are the probabilities for each z-score:

Question	z-score	Probability
5	1.2800	0.100
6	-1.7300	0.958
7	-0.9200	0.821
8	2.5000	0.006
9	-0.6500	0.742

Explanation:

andard Normal Distribution:

• Recall that the standard normal distribution (SND) is bell-shaped, symmetrical around a mean of 0 with a standard deviation of 1. It represents data where values closer to the mean are more likely, and the probability of extreme values decreases rapidly.
• Z-scores measure how many standard deviations a particular value is away from the mean. A z-score of 1.28 means the value is 1.28 standard deviations above the mean, and -1.73 means it's 1.73 standard deviations below.

Question 5: z-score Greater Than 1.28

Diagram:

• Draw a bell-shaped curve representing the SND.
• Mark the mean () at 0.
• Shade the area to the right of z = 1.28. This represents the probability of a reading greater than 1.28 standard deviations above the mean.

Probability Calculation:

• Using a z-score table or calculator, look up the area to the right of z = 1.28. This value is 0.1000 (to 4 significant figures).
• Therefore, the probability of a reading greater than 1.28 is 0.100 (to 3 significant figures).

Question 6: z-score Greater Than -1.73

Diagram:

• Draw the SND as in Question 5.
• Mark the mean () at 0.
• Shade the area to the right of z = -1.73. This represents the probability of a reading greater than -1.73 standard deviations below the mean (meaning it's above -1.73 standard deviations above the mean).

Probability Calculation:

• Look up the area to the right of z = -1.73. This value is 0.9599 (to 4 significant figures).
• Since the SND is symmetrical, the area to the left of z = 1.73 (which is what we're interested in) is the same as the area to the right of z = -1.73. So, the probability is also 0.9599 (to 4 significant figures), which rounds down to 0.960 (to 3 significant figures).

Question 7: z-score Less Than -0.92

Diagram:

• Draw the SND as in previous questions.
• Mark the mean () at 0.
• Shade the area to the left of z = -0.92. This represents the probability of a reading less than -0.92 standard deviations below the mean.

Probability Calculation:

• Look up the area to the left of z = -0.92. This value is 0.1841 (to 4 significant figures).
• The probability is therefore 0.184 (to 3 significant figures).

Question 8: z-score Less Than 2.50

Diagram:

• Draw the SND as usual.
• Mark the mean () at 0.
• Shade the area to the left of z = 2.50. This represents the probability of a reading less than 2.50 standard deviations below the mean.

Probability Calculation:

• Look up the area to the left of z = 2.50. This value is 0.9938 (to 4 significant figures).
• The probability is therefore 0.994 (to 3 significant figures).

Question 9: z-score Between -0.65 and 1.34

Diagram:

• Draw the SND as usual.
• Mark the mean () at 0.
• Shade the area between z = -0.65 and z = 1.34. This represents the probability of a reading falling within this range.

Probability Calculation:

• Look up the area to the left of z = 1.34. This value is 0.9114 (to 4 significant figures).
• Look up the area to the left of z = -0.65. This value is 0.7425 (to 4 significant figures).