1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marizza181 [45]
3 years ago
15

Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally

distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm. For a randomly found shard, find the following probabilities.
a. the thickness is less than 3.0 mm
b. the thickness is more than 7.0 mm
c. the thickness is between 3.0 mm and 7.0 mm
Mathematics
1 answer:
rusak2 [61]3 years ago
4 0

Answer:

(a) The probability that the thickness is less than 3.0 mm is 0.119.

(b) The probability that the thickness is more than 7.0 mm is 0.119.

(c) The probability that the thickness is between 3.0 mm and 7.0 mm is 0.762.

Step-by-step explanation:

We are given that thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.0 millimeters (mm) and a standard deviation of 1.7 mm.

Let X = <u><em>thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village.</em></u>

So, X ~ Normal(\mu=5.0,\sigma^{2} =1.7^{2})

The z-score probability distribution for the normal distribution is given by;

                           Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean thickness = 5.0 mm

           \sigma = standard deviation = 1.7 mm

(a) The probability that the thickness is less than 3.0 mm is given by = P(X < 3.0 mm)

    P(X < 3.0 mm) = P( \frac{X-\mu}{\sigma} < \frac{3.0-5.0}{1.7} ) = P(Z < -1.18) = 1 - P(Z \leq 1.18)

                                                           = 1 - 0.8810 = <u>0.119</u>

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

(b) The probability that the thickness is more than 7.0 mm is given by = P(X > 7.0 mm)

    P(X > 7.0 mm) = P( \frac{X-\mu}{\sigma} > \frac{7.0-5.0}{1.7} ) = P(Z > 1.18) = 1 - P(Z \leq 1.18)

                                                           = 1 - 0.8810 = <u>0.119</u>

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

(c) The probability that the thickness is between 3.0 mm and 7.0 mm is given by = P(3.0 mm < X < 7.0 mm) = P(X < 7.0 mm) - P(X \leq 3.0 mm)

    P(X < 7.0 mm) = P( \frac{X-\mu}{\sigma} < \frac{7.0-5.0}{1.7} ) = P(Z < 1.18) = 0.881

    P(X \leq 3.0 mm) = P( \frac{X-\mu}{\sigma} \leq \frac{3.0-5.0}{1.7} ) = P(Z \leq -1.18) = 1 - P(Z < 1.18)

                                                           = 1 - 0.8810 = 0.119

The above probability is calculated by looking at the value of x = 1.18 in the z table which has an area of 0.881.

Therefore, P(3.0 mm < X < 7.0 mm) = 0.881 - 0.119 = 0.762.

You might be interested in
there are 3 liters of orange juice at a school party. 10 students want to drinkable of the orange juice, and they all want to ge
Softa [21]

Answer:

Each student gets 0.3 liters or 300 milliliters of orange juice.

Step-by-step explanation:

3 liters = 3000 milliliters

3L/10 or 3000ml/10 = 0.3 L or 300 ml

7 0
3 years ago
12 over 50 as a decimal
ivanzaharov [21]
I believe the answer is 0.24
4 0
3 years ago
Read 2 more answers
I could use some help doing this simple math problem lol.
alexira [117]
D:k-9\geq 0 \wedge k\geq0\\&#10;D:k\geq 9 \wedge k\geq0\\&#10;D:k\geq 9\\&#10;\sqrt{k-9}-\sqrt k=-1\\&#10;\sqrt{k-9}=-1+\sqrt k\\&#10;k-9=(-1+\sqrt k)^2\\&#10;k-9=1-2\sqrt k+k\\&#10;2\sqrt k=10\\&#10;\sqrt k =5\\&#10;k=25&#10;&#10;
7 0
3 years ago
Find the value of b in the rhombus below
jeka94
The value of b = 26.
8 0
3 years ago
A bank loaned out $8200, part of it at a rate of 7.9% per year and the rest of it at a rate of 7.4% per year. The total amount o
Lady bird [3.3K]

The amount that the bank loaned out at 7.9% is $1,574.00

How do represent the amounts lent at different rates?

On the assumption that x amount was loaned at 7.9% and that the remaining amount, (8,200-x) was loan out at 7.4%, we can determine the interest charged on each loan as the loan multiplied by the interest rate

interest on 7.9% loan=7.9%*x=0.079x

interest on 7.4% loan=7.4%*(8200-x)

interest on 7.4% loan=606.80-0.074x

total interest=0.079x+606.80-0.074x

total interest=0.005x+606.80

total interest on loans=614.67

614.67=0.005x+606.80

614.67-606.80=0.005x

7.87=0.005x

x=7.87/0.005

x=amount loaned at 7.9%=$1,574.00

y=$8200-$1574

y=$6,626.00

Find out more about bank loan interest rate on:brainly.com/question/20796174

#SPJ1

3 0
1 year ago
Other questions:
  • May someone help me please please please with the right answer
    11·2 answers
  • $0.\overline{5} + 0.19\overline{4}$.
    14·1 answer
  • On a coordinate plane, 2 triangles are shown. The first triangle has points A (1, 4), B (3, 4), C (3, 2). The second triangle ha
    10·2 answers
  • Today there were two members absent from the band
    12·2 answers
  • Spencer has 1/3 pound of nuts he divides them equally into 4 bags what fraction of a pound of nuts is in each bag
    12·1 answer
  • 5•9-10<br> ————<br> 5-(-2).
    11·1 answer
  • Two students, Raymond and Shauna, are trying to get city council members to vote for a new park along the river. 2/6 of the 24 c
    13·2 answers
  • Question 20
    9·1 answer
  • Will the following measurements create a triangle? 25 25 130
    14·1 answer
  • ( 2 x 8 ) - ( 2 x 3 ) = __ x ( 8 - 3 )
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!