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larisa86 [58]
3 years ago
12

An insect measured 1.25cm wich numbeer is less than 1.25?a)1.35, b)1.3, c)1.26 , d)1.2​

Mathematics
1 answer:
Igoryamba3 years ago
5 0
If the length of the insect is 1.25 cm, then 1.2 is less than 1.25. This is because in counting 1.2 comes before 1.25
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You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confide
salantis [7]

Answer:

With​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The​ 95% confidence interval is wider than the​ 90%.

Step-by-step explanation:

We are given that a random sample of 60 home theater systems has a mean price of​$131.00. Assume the population standard deviation is​$18.80.

  • Firstly, the pivotal quantity for 90% 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 price = $131

            \sigma = population standard deviation = $18.80

            n = sample of home theater = 60

            \mu = population mean

<em>Here for constructing 90% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.</em>

<u>So, 90% confidence interval for the population mean, </u>\mu<u> is ;</u>

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

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

                                                  = [131-1.645 \times {\frac{18.8}{\sqrt{60} } } , 131+1.645 \times {\frac{18.8}{\sqrt{60} } } ]

                                                  = [127.01 , 134.99]

Therefore, 90% confidence interval for the population mean is [127.01 , 134.99].

  • Now, the pivotal quantity for 95% 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 price = $131

            \sigma = population standard deviation = $18.80

            n = sample of home theater = 60

            \mu = population mean

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.</em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                                  = [131-1.96 \times {\frac{18.8}{\sqrt{60} } } , 131+1.96 \times {\frac{18.8}{\sqrt{60} } } ]

                                                  = [126.24 , 135.76]

Therefore, 95% confidence interval for the population mean is [126.24 , 135.76].

Now, with​ 90% confidence, it can be said that the population mean price lies in the first interval. With​ 95% confidence, it can be said that the population mean price lies in the second interval. The ​95% confidence interval is wider than the​ 90%.

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3 years ago
Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he
gregori [183]

The probability that he got at least 2 questions correct is 0.756.

Probability is simply how probably something is to appear. every time we're uncertain approximately the final results of an occasion, we can communicate approximately the possibilities of positive outcomes and how in all likelihood they may be. The analysis of occasions ruled through chance is called data.

Basic Probability Rules

  • For any event A, 0 ≤ P(A) ≤ 1
  • The sum of the probabilities of all possible outcomes is 1
  • The Complement Rule
  • Probabilities Involving Multiple Events.
  • Addition Rule for Disjoint Events

Learn more about probability here brainly.com/question/24756209

#SPJ4

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2 years ago
Solve for y: 3y - x = a
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3y - x = a

To solve for y we isolate the y variable.

3y = x + a
y = (x + a)/3
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3 years ago
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