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Luden [163]
3 years ago
14

The highest recorded temperature during the month of July for a given year in Death Valley, California has an approximately norm

al distribution with a mean of 123.8 degrees Fahrenheit and standard deviation of 3.1 deg. F (Weather Source, 2009). What is the probability for a given year that the temperature never exceeds 120 deg. F in a given July in Death Valley? Include leading zero, and state your answer to 3 decimal places.
Mathematics
1 answer:
S_A_V [24]3 years ago
6 0

Answer:

P(X

And we can find this probability using excel or the normal standard tabe and we got:

P(z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:

X \sim N(123.8,3.1)  

Where \mu=123.8 and \sigma=3.1

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using excel or the normal standard tabe and we got:

P(z

You might be interested in
Help me please show how you got the answer
Lilit [14]

Answer:

Firstly you need to put the equation in form of. y =ax+b

Let us do it

We have

2x-2y=18

-2y=18-2x

-y=(18) /2 - (2x)/2

-y =9-x

Mutiply by - to remove it beside y

Y=-9+x

Which is y=x-9

Slope =a=1

Yintercept=b=-9

3 0
3 years ago
Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same wid
swat32

Answer:

difference in area = 16 ft²

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

Step-by-step explanation:

Jacks rectangular patio

width = a

length = 2a - 1

area = lw

where

l = length

w = width

area = 120 ft²

a(2a - 1)

2a² - a - 120 = 0

(a - 8) (2a + 15)

a = 8 or -15/2

Ron's rectangular patio

width = a

length = a + 5

area = lw

area = 104 ft²

a (a + 5) = 104

a² + 5a -104 = 0

(a + 8)  (a - 13)

a = -8 or 13

How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,

120 - 104 = 16 ft²

The value 8 or 13 can be used for a since the width a have to be the same.

if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

if you use 13 the difference i length will be 25 - 18 = 7 ft

6 0
3 years ago
A test consists of 10 true/false questions. To pass the test a student must answer at least 88 questions correctly. If a student
Zanzabum

Answer:

The probability that the student is going to pass the test is 0.0545

Step-by-step explanation:

The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:

P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}

Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2

Then, if the student pass the test with at least 8 questions correct, the probability P of that is:

P = P(8) + P(9) + P(10)

P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})

P = 0.0439 + 0.0097 + 0.0009

P = 0.0545

8 0
3 years ago
the square of a number increased by 5 times the number is equal to 176. find one number for which this could be true
avanturin [10]

Answer:

11 or -16

Step-by-step explanation:

The square of a number increased by 5 times the number is equal to 176.

Let the number be x

Then, x²+5x=176

x²+5x-176=0

We use splitting the middle term method

x²+16x-11x-176=0

x(x+16)-11(x+16)=0

(x-11)(x+16)=0

i.e. either x-11=0 or x+16=0

i.e. either x=11 or x=-16

Hence, the number is either 11 or -16

4 0
3 years ago
Read 2 more answers
A store is having a buy-one-get-one-30%-off sale. During the sale, Christopher
mariarad [96]

Answer:

Step-by-step explanation:

(30*48)/100 = 14.40

48 - 14.40 = $ 33.60

48 + 33.60 = $ 81.60

6 0
3 years ago
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