The table below shows the probability distribution of the types of food purchased by students from the school cafeteria. What is the probability a student has purchased Caesar salad?

(2 points)
0.17
Suppose houses are available for purchase during construction of a new housing development. Two different types of houses are being built: rancher and colonial. The mean price of the ranchers is $319,000 with a standard deviation of $12,000. The mean price of the colonials is $405,000 with a standard deviation of $18,500.

8. Find the combined mean price of the two different types of houses. (2 points)
$362,000

9. Find the combined standard deviation of the two different types of houses. (2 points)
$22,051.0771 or $22,051.08

10. The purchase price for the colonial houses is reduced by $10,000. What would be the new mean for the colonial houses? (2 points)
$357,000

11. If the purchase price for the colonial houses is reduced by $10,000, how much would the standard deviation for the colonial houses change? (2 points)

To find the probability that a student has purchased Caesar salad, we need to look at the table showing the probability distribution of types of food purchased. Assuming that the table has been provided, you should find the row corresponding to Caesar salad and locate the probability value in that row.

In the given question, the probability value is not mentioned in the table. Therefore, we cannot determine the probability without this information. Please provide the probability values associated with each type of food in the table, and I will be able to calculate the probability of a student purchasing Caesar salad.

Moving on to the second set of questions regarding the housing development:

8. To find the combined mean price of the two different types of houses, you add the two mean prices together and divide by the number of types of houses. In this case, the calculation would be: ($319,000 + $405,000) / 2 = $362,000.

9. To find the combined standard deviation of the two different types of houses, you first square the individual standard deviations, add them together, divide by the number of types of houses, and then take the square root of the result. Using the given standard deviations ($12,000 and $18,500), the calculation would be: sqrt((($12,000^2) + ($18,500^2))/2) = $22,051.0771 or $22,051.08 (rounded to two decimal places).

10. If the purchase price for the colonial houses is reduced by $10,000, the new mean for the colonial houses would be the original mean minus $10,000. Using the given mean price for the colonials ($405,000), the new mean would be: $405,000 - $10,000 = $395,000.

11. The standard deviation does not change when a constant value is added or subtracted from each data point. Therefore, reducing the purchase price for the colonial houses by $10,000 would not affect the standard deviation. The standard deviation would remain the same as it was before the reduction.