Answer:
The probability that all 70 messages are transmitted in less than 12 minutes is 0.117.
Step-by-step explanation:
Let <em>X</em> = the transmission time of each message.
The random variable <em>X</em> follows an Exponential distribution with parameter <em>λ</em> = 5 minutes.
The expected value of <em>X</em> is:

The variance of <em>X</em> is:

Now define a random variable <em>T</em> as:
T = X₁ + X₂ + ... + X₇₀
According to a Central limit theorem if a large sample (<em>n</em> > 30) is selected from a population with mean μ and variance σ² then the sum of random variables <em>X</em> follows a Normal distribution with mean,
and variance,
.
Compute the probability of T < 12 as follows:

*Use a <em>z</em>-table for the probability.
Thus, the probability that all 70 messages are transmitted in less than 12 minutes is 0.117.
Answer:
Last option 527.7 ft
Step-by-step explanation:
From the diagram attached we can see the angle of depression is 80.2 which is equal to ∠ACB (alternate angles)
Height of the deck AB = 520 ft. and we have to calculate the distance H between the tourist and her friend.
Sin ∠ACB = 
Now we apply sin rule sin 80.2 = 


So the tourist and her friend are 527.7 ft apart.
Answer:
The probability that the two sweet will not be same type is 
Step-by-step explanation:
P(two sweets not same) = 1 - P( two sweets will be same)
There are 3 possible outcomes where two sweets will be same.
1. it can be two liquor-ice, 2. it can be 2 mint and 3. it can be two humbug
P(two liquor-ice) 
P(two mint) 
P(tow humbug) 
Now we have:
P(two sweets not same) = 1 - P( two sweets will be same)


Therefore, the probability that the two sweet will not be same type is 