Relationship among Exponential, Gamma, and Normal distribution. I am studying stochastic processes where I stumbled upon the theorem that says the sum of exponential distributions is gamma distribution. However, from the central limit theorem, we know that sum of a sufficiently large number of IID random variables converges to Normal distribution. So is the following relationship always true?

Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes?

Write formula for the sequence of -4, 0, 8, 20, 36, 56, 80, where the order of f(x) is 0, 1, 2, 3, 4, 5, 6 respectively

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.n=20​,
p=0.7​,
x=19
P(19)=

In binomial probability distribution, the dependents of standard deviations must includes.
a) all of above.
b) probability of q.
c) probability of p.
d) trials.

The probability that a man will be alive in 25 years is 3/5, and the probability that his wifewill be alive in 25 years is 2/3
Determine the probability that both will be alive

How many different ways can you make change for a quarter??
(Different arrangements of the same coins are not counted separately.)

One hundred people line up to board an airplane that can accommodate 100 passengers. Each has a boarding pass with assigned seat. However, the first passenger to board has misplaced his boarding pass and is assigned a seat at random. After that, each person takes the assigned seat. What is the probability that the last person to board gets his assigned seat unoccupied?
A) 1
B) 0.33
C) 0.6
D) 0.5

The value of $(243{)}^{-<!--\; -\; -->\frac{2}{5}}$ is _______.
A)9
B)$\frac{1}{9}$
C)$\frac{1}{3}$
D)0

1 octopus has 8 legs. How many legs does 3 octopuses have?
A) 16
B 24
C) 32
D) 14

From a pack of 52 cards, two cards are drawn in succession one by one without replacement. The probability that both are aces is...

A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace is A$\frac{9}{20}$ B$\frac{3}{16}$ C$\frac{1}{6}$ D$\frac{1}{9}$

You spin a spinner that has 8 equal-sized sections numbered 1 to 8. Find the theoretical probability of landing on the given section(s) of the spinner. (i) section 1 (ii) odd-numbered section (iii) a section whose number is a power of 2. [4 MARKS]

If A and B are two independent events such that $P(A)>0.5,P(B)>0.5,P(A\cap <!--\; \cap \; -->\stackrel{¯<!--\; ¯\; -->}{B})=\frac{3}{25}P(\stackrel{¯<!--\; ¯\; -->}{A}\cap <!--\; \cap \; -->B)=\frac{8}{25}$, then the value of $P(A\cap <!--\; \cap \; -->B)$ is
A) $\frac{12}{25}$
B) $\frac{14}{25}$
C) $\frac{18}{25}$
D) $\frac{24}{25}$

The unit of plane angle is radian, hence its dimensions are
A) $[M^0{L}^0{T}^0]$
B) $[M^1{L}^{-<!--\; -\; -->1}{T}^0]$
C) $[M^0{L}^1{T}^{-<!--\; -\; -->1}]$
D) $[M^1{L}^0{T}^{-<!--\; -\; -->1}]$

Clinical trial tests a method designed to increase the probability of conceiving a girl. In the study, 340 babies were born, and 289 of them were girls. Use the sample data to construct a 99​% confidence interval estimate of the percentage of girls born?