Answer:
There is strong evidence that less than 87% of the orders are delivered in less than 10 minutes.
Decision rule: Reject the null hypothesis if (P-value < level of significance)
Test statistic z=-2.70
Decision: Reject the null hypothesis (0.003<0.010)
Step-by-step explanation:
In this question we have to test an hypothesis.
The null and alternative hypothesis are:

The significance level is assumed to be 0.01.
The sample of size n=80 gives a proportion of p=61/80=0.7625.
The standard deviation is:

The statistic z is then

The P-value is

The P-value (0.003) is smaller than the significance level (0.010), so the effect is significant. The null hypothesis is rejected.
There is strong evidence that less than 87% of the orders are delivered in less than 10 minutes.
Decision rule: Reject the null hypothesis if (P-value < level of significance)
Test statistic z=-2.70
Decision: Reject the null hypothesis (0.003<0.010)
Since we know that a number is divisible by 3 if the sum of all digits is divisible by 3.
Let us check which digits will make 371? divisible by 3.

11 is not divisible by 3.
Now let us check other digits as well.
12 is divisible by 3.

15 is also divisible by 3.

18 is divisible by 3 as well.
Therefore, 1, 4 and 7 in tenth place will make our number divisible by 3 and our numbers will be 3711, 3714 and 3717.
Answer:
68
Step-by-step explanation:
6.8 × 
= 68
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)