Final answer:
To estimate the percentage of Caribbean weddings that fall within specific cost ranges, we can use the properties of the normal distribution. Given a mean of $9000 and a standard deviation of $715, we can calculate the z-scores for the given values and use the z-table to find the corresponding probabilities. Using this approach, we can determine the percentage of Caribbean weddings that fall between specific cost ranges.
Step-by-step explanation:
To estimate the percentage of Caribbean weddings that fall within specific cost ranges, we can use the properties of the normal distribution. Given a mean of $9000 and a standard deviation of $715, we can calculate the z-scores for the given values and use the z-table to find the corresponding probabilities:
(a) To find the percentage of weddings between $6855 and $11145, we calculate the z-scores for these values: z1 = (6855 - 9000) / 715 = -3.16 and z2 = (11145 - 9000) / 715 = 1.61. Using the z-table, we find the area to the left of z1 (which corresponds to weddings below $6855) and subtract it from the area to the left of z2 (which corresponds to weddings below $11145) to find the percentage of weddings between the two values.
(b) To find the percentage of weddings above $11145, we calculate the z-score for this value: z = (11145 - 9000) / 715 = 1.61. Using the z-table, we find the area to the right of z (which corresponds to weddings above $11145).
(c) To find the percentage of weddings below $8285, we calculate the z-score for this value: z = (8285 - 9000) / 715 = -1.00. Using the z-table, we find the area to the left of z (which corresponds to weddings below $8285).
(d) To find the percentage of weddings between $8285 and $11145, we calculate the z-scores for these values: z1 = (8285 - 9000) / 715 = -1.00 and z2 = (11145 - 9000) / 715 = 1.61. Using the z-table, we find the area to the left of z1 (which corresponds to weddings below $8285) and subtract it from the area to the left of z2 (which corresponds to weddings below $11145) to find the percentage of weddings between the two values.