Find average of all prime numbers between 60 and 90

Options

A. 72
B. 74.7
C. 74
D. 73.6

Answer

To find the average of all prime numbers between 60 and 90, we will follow these steps:

### Step 1: Identify the prime numbers between 60 and 90
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. We will list the prime numbers in the range from 60 to 90.

- The prime numbers between 60 and 90 are: **61, 67, 71, 73, 79, 83, 89**.

### Step 2: Count the number of prime numbers
Next, we need to count how many prime numbers we have identified.

- We have a total of **7 prime numbers**: 61, 67, 71, 73, 79, 83, and 89.

### Step 3: Calculate the sum of the prime numbers
Now, we will calculate the sum of these prime numbers.

- Sum = 61 + 67 + 71 + 73 + 79 + 83 + 89

Calculating the sum:
- 61 + 67 = 128
- 128 + 71 = 199
- 199 + 73 = 272
- 272 + 79 = 351
- 351 + 83 = 434
- 434 + 89 = 523

So, the total sum of the prime numbers is **523**.

### Step 4: Calculate the average
To find the average, we divide the sum of the prime numbers by the total number of prime numbers.

- Average = Total Sum / Number of Prime Numbers
- Average = 523 / 7

Calculating the average:
- Average = 74.71428571428571 (approximately 74.71 when rounded to two decimal places)

### Final Answer
The average of all prime numbers between 60 and 90 is approximately **74.71**.

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