A camera store sells 40 pairs of binoculars per week on average with a standard deviation of 6. What is the probability that the store will sell more than 52 pairs binoculars in any week?

8.28%

3.57%

7.24%

2.28%

4.55%

7.24%

To find the probability that the store will sell more than 52 pairs of binoculars in any week, we need to calculate the z-score and use the standard normal distribution table.

Step 1: Calculate the z-score
Z = (x - μ) / σ
where x = 52 (number of pairs of binoculars), μ = 40 (mean), and σ = 6 (standard deviation)

Z = (52 - 40) / 6
Z = 12 / 6
Z = 2

Step 2: Look up the z-score in the standard normal distribution table
The z-score of 2 corresponds to a probability of 0.9772.

Step 3: Calculate the probability of selling more than 52 pairs of binoculars
Since we want to find the probability of selling more than 52 pairs, we need to subtract the probability from 1.
Probability = 1 - 0.9772
Probability ≈ 0.0228

Therefore, the probability that the store will sell more than 52 pairs of binoculars in any week is approximately 2.28%.

The correct answer is 2.28%.

To find the probability that the store will sell more than 52 pairs of binoculars in any given week, we can use the concept of the standard deviation.

First, let's calculate the z-score, which measures how many standard deviations an observation is away from the mean. We can use the formula:

z = (x - μ) / σ

Where:
x = the value we are interested in (52)
μ = the mean (40)
σ = the standard deviation (6)

Substituting the values into the formula:

z = (52 - 40) / 6
z = 2 / 6
z ≈ 0.3333

Next, we need to find the probability associated with this z-score. We can look up this value in a standard normal distribution table or use a calculator.

The probability of selling more than 52 pairs of binoculars in a week is equal to 1 minus the probability of selling less than or equal to 52 pairs. Mathematically, we can express this as:

P(x > 52) = 1 - P(x ≤ 52)

Using the z-score of 0.3333, we can find the corresponding probability from the standard normal distribution table or a calculator.

Looking up the z-score of 0.3333 in the table or using a calculator, we find that the corresponding probability is approximately 0.6295.

Finally, we can calculate the probability of selling more than 52 pairs of binoculars in a week:

P(x > 52) = 1 - P(x ≤ 52)
P(x > 52) = 1 - 0.6295
P(x > 52) ≈ 0.3705

So, the probability that the store will sell more than 52 pairs of binoculars in any given week is approximately 0.3705, which is equivalent to 37.05%.

None of the options provided (8.28%, 3.57%, 7.24%, 2.28%, 4.55%) match the correct answer.