The table shows the last holiday destination of 60 people.

An example problem in a Statistics textbook asked to find the probability of dying when making a skydiving jump.

MArishka [77]

Answer:

(a) 0.999664

(b) 15052

Step-by-step explanation:

From the given data of recent years, there were about 3,000,000 skydiving jumps and 21 of them resulted in deaths.

So, the probability of death is $\frac{21}{3000000}==0.000007$ .

Assuming, this probability holds true for each skydiving and does not change in the present time.

So, as every skydiving is an independent event having a fixed probability of dying and there are only two possibilities, the diver will either die or survive, so, all skydiving can be regarded as is Bernoulli's trial.

Denoting the probability of dying in a single jump by $q$ .

$q=7\times 10^{-6}=0.000007$ .

So, the probability of survive, $p=1-q$

$\Rightarrow p=1-7\times 10^{-6}=0.999993.$

(a) The total number of jump he made, n=48

Using Bernoulli's equation, the probability of surviving in exactly 48 jumps (r=48) out of 48 jumps (n=48) is

$=\binom(n,r)p^rq^{n-r}$

$=\binom(48,48)(0.999993)^{48}(0.000007)^{48-48}$

$=(0.999993)^{48}=0.999664$ (approx)

So, the probability of survive in 48 skydiving is 0.999664,

(b) The given probability of surviving =90%=0.9

Let, total $n$ skydiving jumps required to meet the surviving probability of 0.9.

So, By using Bernoulli's equation,

$0.9=\binom {n }{r} p^rq^{n-r}$

Here, r=n.

$\Rightarrow 0.9=\binom{n}{n}p^nq^{n-n}$

$\Rightarrow 0.9=p^n$

$\Rightarrow 0.9=(0.999993)^n$

$\Rightarrow \ln(0.9)=n\ln(0.999993)$ [ taking $\log_e$ both sides]

$\Rightarrow n=\frac {\ln(0.9)}{\ln(0.999993)}$

$\Rightarrow n=15051.45$

The number of diving cant be a fractional value, so bound it to the upper integral value.

Hence, the total number of skydiving required to meet the 90% probability of surviving is 15052.

3 0

2 years ago

Triangles Q R S and X Y Z are shown. Angles Q S R and X Z Y are right angles. Angles Q R S and X Y Z are congruent. The length o

kumpel [21]

Answer:

Three-fourths

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

so

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

$\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}$

∠Q≅∠X

∠R≅∠Y

∠S≅∠Z

<em>In the right triangle XYZ</em>

Find the tangent of angle X

$tan(X)=\frac{YZ}{XZ}$ ---> opposite side angle X divided by adjacent side angle X

substitute the given values

$tan(X)=\frac{9}{12}$

Simplify

$tan(X)=\frac{3}{4}$

Remember that

∠Q≅∠X

so

$tan(Q)=tan(X)$

therefore

$tan(Q)=\frac{3}{4}$ ---->Three-fourths

7 0

1 year ago

Read 2 more answers

A ball is thrown down from a balcony with a vertical velocity (in ft/s) given by

fenix001 [56]

Answer:

–90 < –32t – 10 < –58

Step-by-step explanation:

We want the velocity to be BETWEEN -90 and -58.

Whenever we need a quantity, let it be A, to be between two numbers, p and q (p is less than q), we can write it as:

p < A < q

Similarly, here we need the velocity, -32t-10 to be BETWEEN -90 and - 58 (with -90 being the smaller number). Thus we can write:

–90 < –32t – 10 < –58

This is the correct choice, 2nd choice.

4 0

1 year ago

Read 2 more answers

A one story home has a total square footage of 1,200. If 900sq ft of the home has a basement, and 300 sq ft has a slab foundatio

anastassius [24]

Answer:

it has 1200

Step-by-step explanation:

because 900+300=1200

8 0

1 year ago

Read 2 more answers

Benito and Tyler are painting opposite sides of the same fence. Tyler has already painted 19 ½ feet of his side of the fence whe

rewona [7]

Answer:

Part A: The time it will take for both of them to painted equal number of feet is 4.875 minutes

The number of feet Benito will have painted when the two sides have equal length is 73.125 feet

Part B: It is not true that Tyler will finish painting his side of the fence before Benito finishes painting his

Part C: Time to rest is 1.864 minutes

Step-by-step explanation:

The given information are;

The length of fence Tyler already painted when Benito started = 19 ¹/₂ feet

Benito paints 15 feet/minute

Tyler paints 11 feet/minute

Length of fence = 150 feet

Part A:

The time it will take for both of them to painted equal number of feet is given as follows;

11×t + 19.5 = 15×t

4×t = 19.5

t = 19.5/4= 4.875 minutes

The time it will take for both of them to painted equal number of feet = 4.875 minutes

The length Benito will have painted when the two sides have equal length = 15 × 4.875 = 73.125 feet

Part B: The time it will take Tyler to finish painting his side of the fence is given as follows;

11 × t + 19.5 = 150

t = (150 - 19.5)/11 ≈ 11.864 minutes

While the time it will take Benito to finish painting his side of the fence is given as follows;

15 × t = 150

t = 150/15 ≈ 10 minutes

Therefore it is not true that Tyler will finish painting his side of the fence before Benito finishes painting his

Part C: Given that Benito finishes before Tyler, the length of time Benito gets to rest is given as follows;

Time to rest = Time Tyler takes to finish - Time Benito takes to finish

Time to rest = 11.864 - 10 = 1.864 minutes.

5 0

2 years ago