According to the last census (2010), the mean number of people per household in the United States is LaTeX: \mu = 2.58 Assume a standard deviation of LaTeX: \sigma = 0.75σ = 0.75. You plan to take a random sample of 110 households, what is the probability the sample mean household size is between 2.5 and 2.66 people? (round your probabilities to three decimal places)

P(2.50 < Xbar < 2.66) = 0.046

Step-by-step explanation:

We are given that Population Mean, = 2.58 and Standard deviation, = 0.75

Also, a random sample (n) of 110 households is taken.

Let Xbar = sample mean household size

The z score probability distribution for sample mean is give by;

             Z = ~ N(0,1)

So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)

P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar 2.50)

P(Xbar < 2.66) = P( < ) = P(Z < -1.68) = 1 - P(Z  1.68)

                                                              = 1 - 0.95352 = 0.04648

P(Xbar 2.50) = P(  ) = P(Z  -3.92) = 1 - P(Z < 3.92)

                                                              = 1 - 0.99996 = 0.00004  

Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.

first, let's see what the pattern is.

58 - x = 47

46 - x = 36

x = 9

so this means that the term after 25 is 25 - 9:

the next term in the sequence is 16.