Has anyone done the segment one practice exam in geometry

a survey amony freshman at a certain university revealed that the number of hours spent studying the week before final exams was

Marat540 [252]

Answer:

Probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

Step-by-step explanation:

We are given that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15.

A sample of 36 students was selected.

Let $\bar X$ = sample average time spent studying

The z-score probability distribution for sample mean is given by;

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

where, $\mu$ = population mean hours spent studying = 25 hours

$\sigma$ = standard deviation = 15 hours

n = sample of students = 36

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the average time spent studying for the sample was between 29 and 30 hours studying is given by = P(29 hours < $\bar X$ < 30 hours)

P(29 hours < $\bar X$ < 30 hours) = P( $\bar X$ < 30 hours) - P( $\bar X$ $\leq$ 29 hours)

P( $\bar X$ < 30 hours) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }$ < $\frac{ 30-25}{\frac{15}{\sqrt{36} } }} }$ ) = P(Z < 2) = 0.97725

P( $\bar X$ $\leq$ 29 hours) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }$ $\leq$ $\frac{ 29-25}{\frac{15}{\sqrt{36} } }} }$ ) = P(Z $\leq$ 1.60) = 0.94520

So, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 and x = 1.60 in the z table which has an area of 0.97725 and 0.94520 respectively.

Therefore, P(29 hours < $\bar X$ < 30 hours) = 0.97725 - 0.94520 = 0.0321

Hence, the probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

7 0

3 years ago

Find the area of the shaded region.

Iteru [2.4K]

Keeping in mind that the area of a rectangle is simply width * length, if we get the area of the larger rectangle, and then subtract the area of the smaller rectangle, we're in effect making a hole in the larger rectangle's area and thus what's leftover is the shaded area.

$\bf \stackrel{\textit{area of the larger rectangle}}{(2x+2)(3x-4)}~~-~~\stackrel{\textit{area of the smaller rectangle}}{(x-3)(x-6)}
\\\\\\
\stackrel{FOIL}{6x^2-2x-8}~~~~-\stackrel{FOIL}{(x^2-9x+18)}\implies 6x^2-2x-8-x^2+9x-18
\\\\\\
5x^2+7x-26$

4 0

3 years ago

Help me find the answer for D and A please do it step by step for D and A

Vilka [71]

All triangles equal 180 degrees
92 + 50 = 142
180 - 142 = 38
Angle A equals 38 degrees

Angle 92 and Angle d Are supplementary which means that both angles added together equals 180
180-92 = 88
Angle d = 88 degrees

4 0

3 years ago

What is the value of -3r+ 8 when r=4

denis23 [38]

Answer: -4.

Explanation: Because -3*4=-12. -12+8=-4.

6 0

2 years ago

Lila deposits her earnings from teaching children in a bank account. She has the peace of mind that her money will remain safe i

liberstina [14]

Answer: Lila is incorrect about transferring money through checks.

Step-by-step explanation: If Lila transfers money through checks then she is adding money to her bank account funds and increasing her interests if she leaves the money there for a while.

6 0

3 years ago