I need explanation for this please

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

2 years ago

Find the value of angle y?

tankabanditka [31]

Value of angle Y is 180-51

8 0

2 years ago

Fill in the boxes please

IRINA_888 [86]

Answer:

x=12, DO=45O, G=45, DG=90

Step-by-step explanation:

Mid point means both lenghts are equal

4x-3=2x+21

2x=24

X=12

-----------------

1)4(12)-3=48-3=45

2)2(12)+21=24+21=45

-----------------------------

DO=45

OG=45

DG=90

4 0

3 years ago

Read 2 more answers

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of pho

Semenov [28]

Answer:

What 108 represents here is that the total number of phones she has to fix each week is 108 phones

Step-by-step explanation:

The linear equation is

P = 108-23d

compare this with the general form;

y = mx + c

we have;

P = -23d + 108

We can see that 108 represents the y-intercept in this case

The x-value at the y-intercept is 0

So what this mean is that the number of phones she has to fix each week is 108

7 0

2 years ago

A well know Statistical Institution claims that the average College tuition for a law degree costs at least thirty five thousand

kirill [66]

Step-by-step explanation:

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ = 35000

Alternative Hypothesis, Ha: μ < 35000

Test statistic,

z = (xbar - mu)/(sigma/sqrt(n))

z = (33450 - 35000)/(5978/sqrt(50))

z = -1.83

P-value Approach

P-value = 0.0336

As P-value >= 0.02, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the average College tuition for a law degree costs at least thirty five thousand dollars.

4 0

2 years ago