Answer:
Step-by-step explanation:
<u>Use of formula:</u>
- P(A and B) = P(A)*P(B|A) and
- P(A and B) = P(B)*P(A|B)
<u>According to above and based on given:</u>
- P(A)P(B|A) = P(B)P(A|B)
- P(B|A) = P(A|B)*P(B)/P(A)
- P(B|A) = 0.20*0.40/0.25 = 0.32
#4)
cross multiply
2(8x+10) = 4 * 5x
16x + 20 = 20x
4x = 20
x = 5
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)
Apply Pythagoras:
length = sqrt( (10--4)² + (6-3)² ) = sqrt(205)
