Question 1192123
Here's how to solve this problem using the binomial probability formula:

**1. Define the variables:**

* n = 46 (sample size)
* p = 0.02 (probability of a battery not meeting specifications)
* k = number of batteries not meeting specifications (0, 1, or 2 for acceptance)

**2. Calculate the probabilities:**

We need to calculate the probability of 0, 1, or 2 batteries not meeting specifications and then add these probabilities together. The binomial probability formula is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

Where nCx is the number of combinations of n items taken x at a time (also written as "n choose x").

* P(0) = (46C0) * (0.02)^0 * (0.98)^46 ≈ 0.396
* P(1) = (46C1) * (0.02)^1 * (0.98)^45 ≈ 0.372
* P(2) = (46C2) * (0.02)^2 * (0.98)^44 ≈ 0.168

**3. Add the probabilities:**

P(acceptance) = P(0) + P(1) + P(2) ≈ 0.396 + 0.372 + 0.168 ≈ 0.936

**Answer:**

The probability that the entire shipment will be accepted is approximately 0.936.