To solve this, we need to calculate the probability that a shipment of ibuprofen tablets is accepted under the given sampling plan, where the acceptance rule is:

• Randomly select 29 tablets.
• Accept the shipment if at most 1 tablet is defective.

The shipment is accepted if 0 or 1 defective tablet is found in the sample of 29. The number of defective tablets follows a binomial distribution, where:

• $n = 29$ (the sample size),
• $p = 0.01$ (the probability that any individual tablet is defective),
• $X$ is the random variable representing the number of defective tablets in the sample.

The probability that exactly $k$ defective tablets are found follows the binomial probability mass function (PMF):

$P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}$

For this case, the shipment is accepted if $X \leq 1$. So, we need to calculate:

$P(X = 0) + P(X = 1)$

Step 1: Calculate $P(X = 0)$

$P(X = 0) = \binom{29}{0} (0.01)^0 (0.99)^{29} = 1 \cdot (0.99)^{29}$

Using a calculator: $P(X = 0) \approx 0.7397$

Step 2: Calculate $P(X = 1)$

$P(X = 1) = \binom{29}{1} (0.01)^1 (0.99)^{28} = 29 \cdot 0.01 \cdot (0.99)^{28}$

Using a calculator: $P(X = 1) \approx 29 \cdot 0.01 \cdot 0.7397 \approx 0.2145$

Step 3: Calculate the total probability

$P(\text{accept shipment}) = P(X = 0) + P(X = 1) = 0.7397 + 0.2145 = 0.9542$

Thus, the probability that the shipment will be accepted is approximately:

$P(\text{accept shipment}) = 0.9542$

So, the final answer is:

$\boxed{0.9542}$

Would you like any further details or explanations on the calculation? Here's a set of related questions for further study:

1. What is the expected number of defective tablets in the sample of 29?
2. How would the acceptance probability change if the defect rate were 5% instead of 1%?
3. What is the standard deviation of the number of defective tablets in the sample?
4. How does the binomial distribution behave when $n$ becomes very large and $p$ becomes very small?
5. What are the implications of changing the acceptance criteria (e.g., accepting shipments with 2 defective tablets instead of 1)?

Tip: When calculating binomial probabilities, always use the binomial formula directly for small values of $n$, but for large $n$ and small $p$, consider using the Poisson approximation.