A car manufacturer crash tests a certain model of car and measures the impact force. The test and model in question produce impact forces that are normally distributed with a mean of 30 metric tons and a standard deviation of 1.5 metric tons. Suppose that the manufacturer tests a random sample of 3 cars and calculates the sample mean impact force. Assume that the cars in the sample are independent. What will be the shape of the sampling distribution of the sample mean impact force?

Approximately Normal

Step-by-step explanation:

Since the population is normally distributed, the sampling distribution of the sample mean will also be normally distributed, even when the sample size is small.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15