Answer:
95% confidence interval for the difference between the average mass of eggs in small and large nest is between a lower limit of 0.81 and an upper limit of 2.39.
Step-by-step explanation:
Confidence interval is given by mean +/- margin of error (E)
Eggs from small nest
Sample size (n1) = 60
Mean = 37.2
Sample variance = 24.7
Eggs from large nest
Sample size (n2) = 159
Mean = 35.6
Sample variance = 39
Pooled variance = [(60-1)24.7 + (159-1)39] ÷ (60+159-2) = 7619.3 ÷ 217 = 35.11
Standard deviation = sqrt(pooled variance) = sqrt(35.11) = 5.93
Difference in mean = 37.2 - 35.6 = 1.6
Degree of freedom = n1+n2 - 2 = 60+159-2 = 217
Confidence level = 95%
Critical value (t) corresponding to 217 degrees of freedom and 95% confidence level is 1.97132
E = t×sd/√(n1+n2) = 1.97132×5.93/√219 = 0.79
Lower limit = mean - E = 1.6 - 0.79 = 0.81
Upper limit = mean + E = 1.6 + 0.79 = 2.39
95% confidence interval for the difference in average mass is (0.81, 2.39)
Answer:
Marion has 34 rocks and Vondra has 17 rocks
Step-by-step explanation:
1. 51 ÷ 3 = 17
2. Because Marion has 2 times the amount of rocks as Vondra you have do 17 × 2 = 34
3. So, Marion has 34 rocks and Vondra has 17 rocks
10+5x=50
subtract ten from both sides
5x=40
divide five from both sides
x=8
samuel will need to paint 8 additional rooms
Answer:
1320
Step-by-step explanation:
880/8 = 110
12x110 = 1320
Answer:
x = 6
y = 1
Step-by-step explanation:
to solve this system of equation we say let
2x + 3y = 15 .......................... equation 1
x - 3y = 3.................................. equation 2
from equation 2
x - 3y = 3.................................. equation 2
x = 3 + 3y.................................... equation3
substitute for x in equation 1
2x + 3y = 15 .......................... equation 1
2(3+3y) + 3y = 15
6 + 6y + 3y = 15
9y = 15 -6 ................................... combining the like terms
9y = 9
divide both sides by the coefficient of y
9y/9 = 9/9
y =1
put y = 1 in equation 3
x = 3 + 3y.................................... equation3
x = 3 + 3(1)
x = 3 +3
x = 6
therefore the value of x is 6 and y is 1 respectively
