Solve for x, y, and z

See below.

Step-by-step explanation:

x = 180 - (36+60)

= 180 - 96

= 84 degrees.

y = 180 - 84 = 96 degrees.

z = 180 - (96 + 22)

= 180 - 118

= 62 degrees,

x = 84, y = 96, z = 62

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

x = 180 - (60 + 36) = 180 - 96 = 84

x and y lie on a straight line and sum to 180° , then

y = 180 - x = 180 - 84 = 96

z = 180 - (96 + 22) ← angle sum of triangle

z = 180 - 118 = 62

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                          P.Q. =  ~ N(0,1)

where, = sample proportion of students received a passing grade = 77%

           n = sample of tests = 40

           p = population proportion

Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5%

                                           level of significance are -2.5758 & 2.5758}  

P(-2.5758 < < 2.5758) = 0.99

P( < < ) = 0.99

P( < p < ) = 0.99

99% confidence interval for p = [ , ]

 = [ , ]

 = [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414