Question

A carnival ride has cars that each hold 4 adult passengers. The weights of the passengers for this ride are normally distributed with a mean of 65 kg and a standard deviation of 12 kg. Assume that the weights of passengers are independent from each other. Let t be the total weight of 4 randomly selected adult passengers for this ride. Find the probability that the total weight is less than 242 kg. You may round your answer to two decimal places. a. 0.34 b. 0.40 c. 0.46 d. 0.52

Answer 1

The probability that the total weight of 4 randomly selected adult passengers is less than 242 kg is approximately 0.2266.

None of the given options is correct

Step-by-step explanation:

to find the probability that the total weight of 4 randomly selected adult passengers is less than 242 kg, we need to calculate the z-score and then find the corresponding probability.

1. Calculate the mean and standard deviation of the total weight of 4 passengers:

- Mean (μ) = 4 * 65 kg = 260 kg

- Standard deviation (σ) = √(4 * (12 kg)^2) = 24 kg

2. Calculate the z-score using the formula: z = (x - μ) / σ, where x is the desired value.

- z = (242 kg - 260 kg) / 24 kg = -0.75

3. Use the standard normal distribution table or a calculator to find the probability corresponding to the z-score of -0.75.

Based on the standard normal distribution table, the probability that a z-score is less than -0.75 is approximately 0.2266.

None of the given options is correct