Suppose you roll a 6-faced die 90 times. About how many times would you expect to get a 5?

Suppose a simple random sample of size nequals81 is obtained from a population with mu equals 79 and sigma equals 18. (a) Descr

Daniel [21]

Answer:

(a) The sampling distribution of $\overline{X}$ = Population mean = 79

(b) P ( $\overline{X}$ greater than 81.2 ) = 0.1357

(c) P ( $\overline{X}$ less than or equals 74.4 ) = .0107

(d) P (77.6 less than $\overline{X}$ less than 83.2 ) = .7401

Step-by-step explanation:

Given -

Sample size ( n ) = 81

Population mean $(\nu)$ = 79

Standard deviation $(\sigma )$ = 18

(a) Describe the sampling distribution of $\overline{X}$

For large sample using central limit theorem

the sampling distribution of $\overline{X}$ = Population mean = 79

(b) What is Upper P ( $\overline{X}$ greater than 81.2 ) =

$P(\overline{X}> 81.2)$ = $P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}> \frac{81.2 - 79}{\frac{18}{\sqrt{81}}})$

= $P(Z> 1.1)$

= $1 - P(Z< 1.1)$

= 1 - .8643 =

= 0.1357

(c) What is Upper P ( $\overline{X}$ less than or equals 74.4 ) =

$P(\overline{X}\leq 74.4)$ = $P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{74.4- 79}{\frac{18}{\sqrt{81}}})$

= $P(Z\leq -2.3)$

= .0107

(d) What is Upper P (77.6 less than $\overline{X}$ less than 83.2 ) =

$P(77.6< \overline{X}< 83.2)$ = $P(\frac{77.6- 79}{\frac{18}{\sqrt{81}}})< P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}\leq \frac{83.2- 79}{\frac{18}{\sqrt{81}}})$

= $P(- 0.7< Z< 2.1)$

= $(Z< 2.1) - (Z< -0.7)$

= 0.9821 - .2420

= 0.7401

3 0

2 years ago

Solve for b2 in A = 1/2 h ( b1 + b2 ), if A = 16, h = 4, and b1 = 3.

Katarina [22]

Hello from MrBillDoesMath!

Answer:

b2 = 5

Discussion:

A = 1/2 h (b1 + b2) .

Substituting A = 16, h = 4, and b1=3 in the above formula gives:

16 = (1/2) (4)( 3 + b2) => (as (1/2)4 = 2) )

16 = 2 ( 3 + b2) => (divide both sides by 2)

8 = (3 + b2) => (subtract 3 from both sides)

8-3 = b2 =>

5 = b2

Check Area formula:

Does A = 16 = (1/2)(4)(3+5) ?

Does 16 = (1/2) (4)(8) ?

Does 16 = (1/2)(32) ? Yes it does so our calculation for b2 is correct

Thank you,

MrB

7 0

2 years ago

When the angle of elevation to the sun is 42 a flagpole casts a shawdow that is 21 ft long

podryga [215]

:):):):):):):):):):):):

7 0

2 years ago

Nate is 10/9/12 years old. How old will he be in 2/1/12 more years

EastWind [94]

The answer is B. 10 9/12 + 2 1/12= 12 10/12. 12÷2=6 10÷2=5 making the answer 12 5/6

5 0

2 years ago

3(x-7)+8=-20<br><br><br><br>can someone explain how to do this step by step

Mrrafil [7]

3(x-7)+8=-20

Multiply the bracket by 3

(3)(x)(3(-7)+8= -20

3x-21+8= -20

3x-13= -20

Move -13 to the other side. Sign changes from -13 to +13.

3x-13+13= -20+13

3x= -7

Divide by 3

3x/3= -7/3

x= -7/3 or in mixed number : -2 1/3

Answer : x= -7/3 or in mixed number : -2 1/3

3 0

3 years ago

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