Is 7/18 rational or irrational

Nady [450]

Product is basically a vocabulary word meaning multiply. 1500 x 1700 gives you a huge number that is 2,550,000.

6 0

2 years ago

. In a study of air-bag effectiveness it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes

jok3333 [9.3K]

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

$P(X = r) = nCr * p^{r} * (1 - p)^{n - r}$

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

5 0

2 years ago

How many artists could be featured in the show?

EleoNora [17]

Well we're just looking at oil paintings so let's say each shows 2 paintings...

30/2 = 15

so at most- 15 artists

7 0

2 years ago

Read 2 more answers

A bag has 9 marbles: 4 are green, 2 are red, and 3 are blue. Melissa chooses a marble at random, and without putting it back, ch

nika2105 [10]

Answer: pr (blue) = 1/3 or 0.33

Pr(green without replacement) = 1/2 = 0.5

Step-by-step explanation:

Probability = number of possible outcomes/ number of total outcomes

Total number of outcomes is the sum of all the marbles, given as 9

Pr ( first marble blue) = no of blue marbles/ total number of marbles

= 3/9 = 1/3 or 0.333

Second marble is chosen without replacement- this means that the total outcome has reduced by 1, total number of marbles has reduced to 8 because there was no replacement.

Pr (second marble is green) = number of green marble/ total number of marbles without replacing the first marble

= 4/8 = 1/2 = 0.5

I hope this helps.

7 0

2 years ago

The diagram shows the net of a juice box. The box is a rectangular prism.

Hoochie [10]

Answer:

269.6 square centimeters

Step-by-step explanation:

The correct question is

The diagram shows the net of a juice box. the box is a rectangular prism. what is the surface area of the juice box? 6.4 cm 4 cm 10.5 cm