Given:
Mean = 7
Observations: 5, 3, 0.5, 4.5, b, 8.5, 9.5

To find:
The value of b

Approach:
To find the value of b, we need to use the formula for the mean. The mean is calculated by summing up all the observations and dividing it by the number of observations.

Step 1: Find the sum of all the observations.
Sum = 5 + 3 + 0.5 + 4.5 + b + 8.5 + 9.5

Step 2: Use the formula for the mean and substitute the given mean value.
7 = (Sum of observations) / (Number of observations)

Step 3: Substitute the sum of observations from step 1 into the formula.
7 = (5 + 3 + 0.5 + 4.5 + b + 8.5 + 9.5) / (Number of observations)

Step 4: Count the number of observations.
There are 7 observations in total.

Step 5: Simplify the equation.
7 = (30 + b) / 7

Step 6: Cross multiply and solve for b.
7 * 7 = 30 + b
49 = 30 + b
49 - 30 = b
b = 19

Answer:
The value of b is 19.

Explanation for finding the new mean:
To find the new mean, we need to decrease each observation by 1 unit and calculate the mean again.

Step 1: Decrease each observation by 1 unit.
New observations: 4, 2, -0.5, 3.5, 18, 7.5, 8.5

Step 2: Find the sum of the new observations.
New sum = 4 + 2 + (-0.5) + 3.5 + 18 + 7.5 + 8.5

Step 3: Count the number of observations.
There are still 7 observations.

Step 4: Use the formula for the mean and substitute the new sum and number of observations.
New mean = (New sum of observations) / (Number of observations)

Step 5: Substitute the new sum of observations from step 2 into the formula.
New mean = (4 + 2 + (-0.5) + 3.5 + 18 + 7.5 + 8.5) / 7

Step 6: Calculate the new mean.
New mean = (43) / 7

Step 7: Simplify the fraction, if possible.
New mean ≈ 6.14

Answer:
The new mean, after decreasing each observation by 1 unit, is approximately 6.14.