Question

1.1 The average outstanding credit card balance for young couples in Namibia is N$650 with a standard deviation of N$420. 1.1.1 What is the probability that a random sample of 100 young couples have a mean credit card balance exceeding N$700? [5] 1.1.2 What is the probability that a random sample of 100 young couples have a mean credit balance between N$625 and N$700?

Answer 1

To calculate the probability that a random sample of 100 young couples have a mean credit card balance exceeding N$700, we can use the Central Limit Theorem and the standard normal distribution.

Step-by-step explanation:

To calculate the probability that a random sample of 100 young couples have a mean credit card balance exceeding N$700, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of sample means from a population with any shape approaches a normal distribution as the sample size increases.

First, we need to standardize the mean of the sampling distribution using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Using the given values, we can calculate the standardized z-score: z = (700 - 650) / (420 / √100) = 50 / 42 = 1.19.

We can then use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.19, which is approximately 0.8821.