Mathematics, 16.06.2020 16:57 mtetwabright1105

Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 80 GPa and 1.8 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.) (a) Calculate P(79 x 81) when n = 25.
(b) How likely is it that the sample mean diameter exceeds 81 when n = 36? You may need to use the appropriate table in the Appendix of Tables to answer this question

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Answer from: tyrique86

(a) Probability that sample mean lies between 79 and 81 is 0.9946.

(b) It is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.

Step-by-step explanation:

We are given that metal sheets of a particular type, its mean value and standard deviation are 80 GPA and 1.8 GPA, respectively.

Suppose the distribution is normal.

Let $\bar X$ = sample mean diameter

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 = 80 GPA

$\sigma$ = standard deviation = 1.8 GPA

n = sample size = 25

(a) Probability that sample mean lies between 79 and 81 is given by = P(79 < $\bar X$ < 81) = P( $\bar X$ < 81) - P( $\bar X$ $\leq$ 79)

P( $\bar X$ < 81) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{81-80}{\frac{1.8}{\sqrt{25} } }$ ) = P(Z < 2.78) = 0.9973

P( $\bar X$ $\leq$ 79) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{79-80}{\frac{1.8}{\sqrt{25} } }$ ) = P(Z $\leq$ -2.78) = 1 - P(Z < 2.78)

= 1 - 0.9973 = 0.0027

The above probability is calculated by looking at the value of x = 2.78 in the z table which has an area of 0.9973.

Therefore, P(79 < $\bar X$ < 81) = 0.9973 - 0.0027 = 0.9946.

(b) Probability that the sample mean diameter exceeds 81 when n = 36 is given by = P( $\bar X$ > 81)

P( $\bar X$ > 81) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{81-80}{\frac{1.8}{\sqrt{36} } }$ ) = P(Z > 3.33) = 1 - P(Z < 3.33)

= 1 - 0.9996 = 0.0004

The above probability is calculated by looking at the value of x = 3.33 in the z table which has an area of 0.9996.

Hence, it is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.

Answer from: Quest

21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.

Answer from: Quest

answer: 323 is how many she has ☃☃⛄❄

step-by-step explanation:

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