Write an equation for the quadratic function whose vertex is (âˆ’2,10) and passes through (1,28)

g An irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the

blagie [28]

Answer:

A 90% confidence interval of the true mean is [$119.86, $123.34].

Step-by-step explanation:

We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.

Also, the standard deviation of the population was $6.36.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

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

where, $\bar X$ = sample mean amount of money spent on textbooks = $121.60

$\sigma$ = population standard deviation = $6.36

n = sample of students = 36

$\mu$ = population mean

Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $121.60-1.645 \times {\frac{6.36}{\sqrt{36} } }$ , $121.60+1.645 \times {\frac{6.36}{\sqrt{36} } }$ ]

= [$119.86, $123.34]

Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].

5 0

2 years ago

A lightbulb has a normally distributed light output with mean 5000 end foot-candles and standard deviation of 50 end foot-candle

Blizzard [7]

To find the specification limit such that only 0.5% of the bulbs will not exceed this limit we proceed as follows;
From the z-table, a z-score of -2.57 cuts off 0.005 in the left tail; given the formula for z-score
(x-μ)/σ
we shall have:
(x-5000)/50=-2.57
solving for x we get:
x-5000=-128.5
x=-128.5+5000
x=4871.50

8 0

2 years ago

Kyle and Cooper are driving. Kyle drives 5 mph faster than Cooper. The same amount of time of Kyle drives 87.1 miles Cooper driv

alexandr1967 [171]

Answer:

Kyle, 67 mph
Cooper, 62 mph

Step-by-step explanation:

Their difference in distance is 87.1 -80.6 = 6.5 miles. Since their difference in speed is 5 mph, it took them (6.5 mi)/(5 mi/h) = 1.3 hours to achieve that separation.

Kyle's speed is 87.1 mi/(1.3 h) = 67 mi/h.

Cooper's speed is 80.6 mi/(1.3 h) = 62 mi/h. (5 mi/h slower)

Kyle is driving 67 mph; Cooper is driving 62 mph.

_____

Alternate solution

The ratio of their speeds is 87.1/80.6 = 67/62. The difference in ratio units happens to equal their difference in miles per hour, so their speeds must be 67 and 62 miles per hour.

4 0

2 years ago

Please help me with these questions

Alina [70]

1 is : d>-9
2 is: k ≥ -18
3 is: g>-1
4 is: n<-40
5 is: w ≤3
That should be correct.

7 0

2 years ago

Read 2 more answers

Find the solutions of the congruence 12x2 + 25x ≡ 10 (mod 11). [Hint: Show the congruence is equivalence to the congruence 12x2

Vlada [557]

Answer:23.89x67

Step-by-step explanation:

5 0

2 years ago