Question

QuenCola, a soft-drink company, knows that it has a 28% market share in one region of the province. QuenCola's marketing department conducts a blind taste test with 100 people at a mall in the region.

Use a normal approximation to calculate that fewer than 25 of these people will choose QuenCola.

Use a normal approximation to calculate the probability that exactly 30 of these people will choose QuenCola.

Answer 1

To calculate the probability that fewer than 25 people will choose QuenCola, use the normal distribution. The probability is approximately 0. To calculate the probability that exactly 30 people will choose QuenCola, use the same formula. The probability is approximately 1.

Step-by-step explanation:

To calculate the probability that fewer than 25 people will choose QuenCola, we need to use the normal distribution. First, we need to find the mean and standard deviation. The mean is 28% of 100, which is 28. The standard deviation is calculated using the formula sqrt((p(1-p)/n)), where p is the proportion and n is the sample size. Plugging in the values, we get sqrt((0.28(1-0.28)/100)) = 0.0484.

Now, we can use the normal distribution to find the probability. To find the probability that fewer than 25 people will choose QuenCola, we need to find the z-score for 25 using the formula z = (x - mean) / standard deviation. Plugging in the values, we get z = (25 - 28) / 0.0484 = -61.9835. Looking up the z-score in a normal distribution table, we find that the probability is approximately 0.

To calculate the probability that exactly 30 people will choose QuenCola, we can use the same formula for the z-score. Plugging in the values, we get z = (30 - 28) / 0.0484 = 41.3223. Looking up the z-score in a normal distribution table, we find that the probability is approximately 1.