What two numbers the quotient is between? then estimate the quotient 789÷8

Previous studies on sleep tendencies report that, on average, an adult American will sleep for 6 hours each night with a standar

Tom [10]

Answer: One sample z test for means

Step-by-step explanation:

From the information given, the sample size is large. It is greater than 30. Again, the population standard deviation is given. This means that the test statistic would be the z score which is determined by the formula

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

The probability value would be determined from the normal distribution table.

Therefore, the hypothesis test that should be used is

One sample z test for means

7 0

2 years ago

40% of Oatypop cereal boxes contain a prize. Hannah plans to keep buying cereal until she gets a prize. What is the probability

aleksley [76]

Answer:

$(0.6)^{n}+n(0.4)(0.6)^{n-1}+\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}$

Step-by-step explanation:

We will use the binomial distribution. Let X be the random variable representing the no. of boxes Hannah buys before betting a prize.

Our success is winning the prize, p =40/100 = 0.4

Then failure q = 1-0.4 = 0.6

Hannah keeps buying cereal boxes until she gets a prize. Then n be no. times she buys the boxes.

P(X ≤ 3) = P(X=0) +P(X=1)+P(X=2)+P(X=3)

= $\binom{n}{0}p^{0}q^{n-0}$ + $\binom{n}{1}p^{1}q^{n-1}$ + $\binom{n}{2}p^{2}q^{n-2}$ + $\binom{n}{3}p^{3}q^{n-3}$

= $q^{n}+npq^{n-1}$ + $\frac{n(n-1)(p)^{2}q^{n-2}}{2}$ + $\frac{n(n-1)(n-2)p^{3}q^{n-3}}{6}$

= $(0.6)^{n}+n(0.4)(0.6)^{n-1}+[tex]\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}$

7 0

2 years ago

Read 2 more answers

Does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?

stiv31 [10]

Given equation of the Circle is ,

$\sf\implies x^2 + y^2 = 25$

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

$\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2$

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

$\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }$