All categories

3 years ago

The time required to finish a test in normally distributed with a mean of 40 minutes

Mathematics

1 answer:

maks197457 [2]3 years ago

8 0

Answer:

84%.

Step-by-step explanation:

Let X be the time in minutes for a student chosen at random to finish the test. $X\sim N(40, 8^{2})$ .

The probability that a student chosen at random finishes the test in less than 48 minutes will represented as

$P(X< 48)$ .

<h3>Method 1: technology</h3>

Evaluate the cumulative normal probability on a calculator, where

The lower bound is 0,
The upper bound is 48,
The mean $\mu = 40$ ,
The standard deviation $\sigma = 8$

$P(X < 48) = 0.8413$ .

<h3>Method 2: z-score table</h3>

$x = 48$ .

$\displaystyle z = \frac{x - \mu}{\sigma} = \frac{48 - 40}{8} = 1$ .

Look up the entry that corresponds to $z = 1.000$ on a z-score table: 0.8413.

In other words,

$P(X < 48) = P(Z < 1) = 0.8413$ .

You might be interested in

A state license plate consists of three letters followed by three digits. If repetition is allowed, how many different license p

Nuetrik [128]

A state license plate consists of three letters followed by three digits. If repetition is allowed, the number of different ways in which license plates are possible is 17,576,000.

<h3>What is a permutation?</h3>

An arrangement of items in a specific order is referred to as a permutation. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection.

Calculation for the permutation -

Three letters are followed by three digits on a state license plate.

26 letters from a to z and 10 numbers from 0 to 9 make up the alphabet.

The potential of arrangements is due to the license plate's composition of three letters and three numerals.

Total ways = 26×26×26×10×10×10

= 17,576,000

Therefore, the number of different ways in which license plates are possible is 17,576,000.

To know more about the permutation, here

brainly.com/question/1216161

#SPJ4

7 0

2 years ago

What is the measure of the circumference of D

Pavel [41]

The circumference Is

тнє ¢ιя¢υмfєяєи¢є ιѕ: 25.13274

нσω тσ fιи∂ ¢ιя¢υмfєяєи¢є: тнє fσямυℓα fσя ¢ιя¢υмfєяєи¢є ιѕ, ¢=2πя

нσρє ι ¢συℓ∂ нєℓρ уσυ

3 0

3 years ago

Read 2 more answers

How do you solve for the slope of a line with the equation ax^2 + bx + c?

ololo11 [35]

<h2>The graph of y = ax^2 + bx + c </h2><h2>A nonlinear function that can be written on the standard form </h2><h2>ax2+bx+c,where a≠0 </h2><h2>All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is </h2><h2> y=x2 </h2><h2> The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate </h2><h2>x=−b2a </h2><h2>The y-coordinate of the vertex is the maximum or minimum value of the function. </h2><h2>a > 0 parabola opens up minimum value </h2><h2>a < 0 parabola opens down maximum value </h2><h2> A rule of thumb reminds us that when we have a positive symbol before x2 we get a happy expression on the graph and a negative symbol renders a sad expression. </h2><h2>The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation </h2><h2>x=−b2a </h2><h2>The y-intercept of the equation is c. </h2><h2> When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.</h2>

3 0

3 years ago

A bicyclist heads east at 10km/h. After she has traveled 24.2 kilometers, another cyclist sets out in the same direction going 3

Alona [7]

We know that the first cyclist has traveled 24.2 km at a speed of 10 km/h. Lets use the equation $time= \frac{distance}{speed}$ to find the time of the first cyclist:
$t= \frac{24.2}{10}$
$t=2.42$
So, we know that she has traveled for 2.42 hours.

We also know that after she has traveled for 2.42 hours another<span> cyclist sets out in the same direction, so if </span> $t$ represents the time of our first cyclist, <span>the time of our second cyclist will be </span> $t-2.42$ .

Now we are going to use the equation $distance=(speed)(time)$ to relate the speeds and times of the two cyclist:
For the first one:
$distance=10t$ equation (1)
For the second one:
$distance=30(t-2.42)$ equation (2)

Replace (1) in (2)
$10t=30(t-2.42)$
The only thing left now is solve for $t$ :
$10t=30t-72.6$
$-20t=-72.6$
$t= \frac{-72.6}{-20}$
$t=3.63$

We can conclude that the second cyclist will catch up the first cyclist after 3.63 hours.

4 0

3 years ago

Susan invests $Z at the end of each year for seven years at an annual effective interest rate of 5%. The interest credited at th

aleksley [76]

Answer:

2.02955

Step-by-step explanation:

Given that:

Susan invests $Z as each year ends for seven years.

So we assume that Z = 1

Susan's accrued value comprises $7 invested each year at a 6 percent annual effective rate.

The cashflow interest:

The cashflow of Susan interest payments are:

Payments Time

0 1

0.05 2

2(0.05) 3

3(0.05) 4

4(0.05) 5

5(0.05) 6

6(0.05) 7

The accumulated value of this cash flow is:

$(0.05)I_{6\%} = (0.05) \dfrac{((1+0.06)_{6\%} - 6)}{0.06} \\ \\ \implies 1.1653$

So Susan accumulated values is:

X = 7 + 1.1653

X = 8.1653

Lori's accumulated value is $14, which she has set aside to plan her cash flow for interest.

The cashflow of Lori interest payments are;

Payments 0 0.025 2(0.025) 3(0.025) ......... 13(0.025)

Time 1 2 3 4 .......... 14

The accumulated value of cash flow is:

$(0.025 )(I)_{3\%} =(0.025) \dfrac{(1+0.03)_{3\%}-13}{0.03}\\ \\= 2.5719$

Now, Lori's accumulated value is:

Y = 14 + 2.5719

Y = 16.5719

Since; Susan value X = 8.1653

Lori's value Y = 16.5719

∴

$\dfrac{Y}{X}= \dfrac{16.5719}{8.1653}$

= 2.02955

7 0

3 years ago