E) Mean = 1.109 minutes, standard deviation = 0.435 minutes
Step-by-step explanation
1. Let's denote the mean as μ and the standard deviation as σ.
2. From the given information, we know that Ricardo spends less than 1 minute brushing his teeth about 40% of the time. This implies that the cumulative probability up to 1 minute is 0.4: P(X ≤ 1) = 0.4.
3. We also know that Ricardo spends more than 2 minutes brushing his teeth 2% of the time. This implies that the cumulative probability beyond 2 minutes is 0.02: P(X > 2) = 0.02.
4. Using a standard Normal distribution table or calculator, we can find the corresponding z-scores for these probabilities:
- For P(X ≤ 1) = 0.4, the z-score is approximately -0.253.
- For P(X > 2) = 0.02, the z-score is approximately 2.055.
5. Now, we can use the z-score formula to find the mean and standard deviation:
- For P(X ≤ 1) = 0.4, the z-score formula is: z = (1 - μ) / σ = -0.253.
- For P(X > 2) = 0.02, the z-score formula is: z = (2 - μ) / σ = 2.055.
6. We can solve these two equations simultaneously to find the values of μ and σ.
7. Solving the equations, we find that the mean is approximately 1.109 minutes and the standard deviation is approximately 0.435 minutes.
Therefore, the correct answer is:
E) Mean = 1.109 minutes, standard deviation = 0.435 minutes.