Answer:
b)The sample size is large enough to use the normal approximation.
Step-by-step explanation:
In one case when sample size is very large usually, the Normal Distribution can be used to calculate an approximate probability of an event. The explanation of this is expained by the Central Limit Theorem which states that when we have a sample size is large, the sampling distribution of means converge to a normal distribution (approximately) and on this way:
The Binomial distribution can be approximated using a Normal Distribution in case when sample size is large. We can consider a sample size is large when we have these two conditions:
np > 10 and n(1-p)>10,
On this case we can assume the random variable
If we check the conditions:
np=493*0.05=24.65>10
n(1-p)=493*(1-0.05)=468.35>10
So then we can conclude that b)the sample size is large enough to use the normal approximation.
If bobby has three more than double the amount of jelly beans that marcus has and if marcus has 30 jelly beans, then bobby will have 63 jelly beans.
Option 4 is correct i.e. <span>The volume of the box is increasing at a rate of 192 cm^3/min.
</span>Given : Volume of the rectangular box = x²h
where x is edge and h is height.
The edge and the height are varying with time, therefore, we write,x = x(t)
h = h(t)
dh/dt = -3 and we shall calculate when x = 4, dx/dt = 2 and when h=15
V = x²h dV/dt = (2x × dx/dt × h) + (x² × dh/dt) dV/dt = 2×4×2×15 + (4)^2 ×(-3) dV/dt = 240 - 48
dV/dt = 192
Because dV/dt is positive, hence the volume is increasing