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LuckyWell [14K]
3 years ago
8

For a confidence level of 85%, find the critical value for a normally distributed variable. The sample mean is normally distribu

ted if the population standard deviation is known.
Mathematics
1 answer:
const2013 [10]3 years ago
7 0

Answer:

The  value is  Z_{\alpha } =  1.439

Step-by-step explanation:

From the question we are told that

   The  confidence level is  C  =  85%  

Generally the level of significance is mathematically represented as

         \alpha =  (100 -  85 )\%

        \alpha =  0.15

Now from the normal distribution table  the critical value  of \alpha is  

     Z_{\alpha } =  1.439

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PLS HELP ME!!!! I WILL MARK U!!!!!<br><br> MATH!!!!
erica [24]

Answer:

-38

Step-by-step explanation:

y=2

z=-17

yz-y^2

(2)(-17)-(2)^2

-34-4

-38

4 0
3 years ago
The mean annual cost of an automotive insurance policy is normally distributed with a mean of $1140 and standard deviation of $3
DerKrebs [107]

Using the normal distribution, it is found that the probabilities are given as follows:

a) 0.8871 = 88.71%.

b) 0.0778 = 7.78%.

c) 0.8485 = 84.85%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

The parameters in this problem are given as follows:

\mu = 1140, \sigma = 310, n = 16, s = \frac{310}{\sqrt{16}} = 77.5

Item a:

The probability is the <u>p-value of Z when X = 1250 subtracted by the p-value of Z when X = 1000</u>, hence:

X = 1250:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{1250 - 1140}{77.5}

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

X = 1000:

Z = \frac{X - \mu}{s}

Z = \frac{1000 - 1140}{77.5}

Z = -1.81

Z = -1.81 has a p-value of 0.0351.

0.9222 - 0.0351 = 0.8871 = 88.71% probability.

Item b:

The probability is <u>one subtracted by the p-value of Z when X = 1250</u>, hence:

1 - 0.9222 = 0.0778 = 7.78%.

Item c:

The probability is the <u>p-value of Z when X = 1220</u>, hence:

Z = \frac{X - \mu}{s}

Z = \frac{1220 - 1140}{77.5}

Z = 1.03

Z = 1.03 has a p-value of 0.8485.

0.8485 = 84.85% probability.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ1

3 0
2 years ago
Etta buys some ribbon and cut it into seven pieces that are the same length each piece is 9 inches long how long was the ribbon
zavuch27 [327]
7 pieces x 9 inches long = The ribbon was 63 inches long.
3 0
3 years ago
Read 2 more answers
The quotient of a number and -5 has a result of 2. What is the number? <br><br> N = ?
Whitepunk [10]

Answer:

-5 × 2 = -10

n ÷ -5 = 2

-10 ÷ -5 = 2

n = -10

6 0
3 years ago
Gabby left the mall and drove north. Violet left 3 hours later, driving 36 mph faster to catch up with Gabby. After 2 hours, she
Archy [21]

Answer:

24mph

Step-by-step explanation:

24 mph times 5 hours = 120 miles

24 mph + 36 mph = 60 mph

60 mph × 2 hours = 120 miles

7 0
3 years ago
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