The number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours. The probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is:

Probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is 0.89435.

Step-by-step explanation:

We are given that the number of hours spent per week on household chores by all adults has a mean of 28 hours and a standard deviation of 7 hours.

Also, sample of 49 adults is given.

Let X = number of hours spent per week on household chores

So, assuming data follows normal distribution; X ~ N()

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

               Z = ~ N(0,1)

where, = mean hours = 28

            = standard deviation = 7 hours

            n = sample of adults = 49

Let = sample mean hours spent per week on household chores

So, probability that the mean hours spent per week on household chores by a sample of 49 adults will be more than 26.75 is given by =P( > 26.75 hours)

    P( > 26.75 hours) = P( > ) = P(Z > -1.25) = P(Z < 1.25)

                                                                     = 0.89435  {using z table}

Therefore, probability that the mean hours spent per week on household chores is more than 26.75 is 0.89435.

step-by-step explanation:

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.