Answer:
t^4
Step-by-step explanation:
Answer:
What are we supposed to find?
Answer:
We should expect 25 generated digits in order to get a fifth "4"
Step-by-step explanation:
For each generated digit, there are only two possible outcomes. Either it is a four, or it is not. The probability of a digit being a 4 is independent of other digits. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
The expetcted number of trials to get r sucesses, with p probability, is given by:

Assume that the calculator will generate a "4" on any given attempt with probability 0.20.
This means that 
How many total generated digits should we expect in order to get a fifth "4"
This is E when r = 5. So

We should expect 25 generated digits in order to get a fifth "4"
16
x
2
+
16
x
=
42
Step 2: Subtract 42 from both sides.
16
x
2
+
16
x
−
42
=
42
−
42
16
x
2
+
16
x
−
42
=
0
For this equation: a=16, b=16, c=-42
16
x
2
+
16
x
+
−
42
=
0
Step 3: Use quadratic formula with a=16, b=16, c=-42.
x
=
−
b
±
b
2
−
4
a
c
2
a
x
=
−
(
16
)
±
(
16
)
2
−
4
(
16
)
(
−
42
)
2
(
16
)
x
=
−
16
±
2944
32
x
=
−
1
2
+
1
4
46
or
x
=
−
1
2
+
−
1
4
46
Answer:
x
=
−
1
2
+
1
4
46
or
x
=
−
1
2
+
−
1
4
46
Answer:
The critical values of r are -0.708 and 0.708.
Step-by-step explanation:
A statistical test is being performed to determine whether there is any linear correlation between two variables.
The hypothesis can be defined as follows:
<em>H</em>₀: There is no linear correlation between two variables, i.e. <em>ρ</em> = 0.
<em>H</em>ₐ: There is a significant linear correlation between two variables, i.e. <em>ρ</em> ≠ 0.
The test statistic is given as follows:

The degrees of freedom of the test is:

The significance level of the test is, <em>α</em> = 0.01.
The critical values of <em>r</em> are:

*Use the <em>r</em> critical value table.
Thus, the critical values of r are -0.708 and 0.708.