I need help with this Alegebra

Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with

soldier1979 [14.2K]

The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

<h3>Probability</h3>

a. Distribution

X ~ N (20 , 6)

b. P(x ≤24)

= P[(x - μ ) / σ (24 - 20) / 6]

= P(z ≤0.67)

= 0.74857

=0.7486

Hence:

Probability = 0.7486

c. P(21 < x < 26)

= P[(21 - 26)/ 6) < (x - μ ) / σ < (24 - 20) / 6) ]

= P(-0.83 < z < 0.67)

= P(z < 0.67) - P(z < -0.)

= 0.74857- 0.2033

= 0.54527

Hence:

Probability =0.54527

d. Using standard normal table ,

P(Z < z) = 66%

P(Z < 0.50) = 0.66

z = 0.50

Using z-score formula,

x = z× σ + μ

x = 0.50 × 6 + 20 = 23

23 Christmas cards

Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.

Learn more about probability here:brainly.com/question/24756209

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8 0

2 years ago

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 8 kg to 28 kg

Furkat [3]

8/28=4/14=2/7
2/7 is simplest form
Not 100% sure but hopefully this helps

5 0

2 years ago

Read 2 more answers

Today, Sean left home at 8 a.m, drove to work, and worked from 9 a.m.5 p.mOn the drive back home, Sean got stuck in slow-moving

kipiarov [429]

Answer:

-20

-10

Step-by-step explanation:

The graph shows that going from home to work was 20km according to the prompt and it took an hour. The two hours he was stuck in traffic was from 5-7pm and he was moving at 10km an hour again, from the graph. (I'm sorry if this isnt the best explanation, I'm better at getting an answer than explaining it).

8 0

2 years ago

Which of the quadratic functions has the narrowest graph?

charle [14.2K]

Answer:

$y=\frac{1}{8}x^2$

Step-by-step explanation:

A quadratic function has the formula ax² + bx + c

To determine if a graph will be narrow or wide, the leading coefficient, a, will be the factor that determines this
The greater the coefficient, the narrower the parabola
The lesser the coefficient, the wider the parabola

Here all of the functions are in the form ax²

In $y=\frac{1}{8}x^{2}$ , our "a" term is $\frac{1}{8}$
In y = -2x², our "a" term is -2
In y = -3x², our "a" term is -3
In $y=\frac{1}{3}x^{2}$ , our "a" term is $\frac{1}{3}$

We can eliminate the two functions with the negative coefficients because they are much smaller than the two functions with the fractions as coefficients, and will therefore open much wider.

We can now compare the two remaining functions, $y=\frac{1}{8}x^2$ and $y=\frac{1}{3}x^2$

Giving the two fractions common denominators would turn them into $y = \frac{3}{24}x^2$ and $y=\frac{8}{24} x^2$
The equation with the larger fraction will be the parabola that is the narrowest. In this case, it is the $y=\frac{8}{24} x^2$ .
Therefore, $y=\frac{1}{8}x^2$ will have the narrowest graph