Final answer:
To find the probability that the sample mean will be less than 295, we can use the Central Limit Theorem and calculate the z-score. Using the z-score, we can find the probability using a standard normal distribution table or calculator.
Step-by-step explanation:
To find the probability that the sample mean will be less than 295, we need to use the Central Limit Theorem. The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
In this case, the sample size is 100, which is considered large enough. We can calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we have: z = (295 - 300) / (45 / sqrt(100)) = -5 / 4.5 = -1.11. We can then look up the z-score in the standard normal distribution table or use a calculator to find the area to the left of -1.11, which is approximately 0.1335. Therefore, the probability that the sample mean will be less than 295 is 0.1335, or 13.35%.