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postnew [5]
3 years ago
12

The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation σ = 25 hours. A random sam

ple of 20 bulbs results in a mean life of 1014 hours. Determine the following: (a) Construct a 95% two-sided CI on the mean life. (b) Construct a 95% lower confidence bound on the mean life.
Mathematics
1 answer:
irina [24]3 years ago
4 0

Answer: a) (1008.34,1019.658) b) (1009.24,1018.76)

Step-by-step explanation:

Since we have given that

n = 75

mean = 1014 hours

Standard deviation = 25 hours

At 95% two sided , z = 1.96

So, confidence interval would be

\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.96\dfrac{25}{\sqrt{75}}\\\\=1014\pm 5.658\\\\=(1014-5.658,1014+5.658)\\\\=(1008.34,1019.658)

(b) Construct a 95% lower confidence bound on the mean life.

z = 1.65

So, confidence interval would be

\bar{x}\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.65\times \dfrac{25}{\sqrt{75}}\\\\=1014\pm 4.76\\\\=(1014-4.76,1014+4.76)\\\\=(1009.24,1018.76)

Hence, a) (1008.34,1019.658) b) (1009.24,1018.76)

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Answer:

h = V/y^2

Step-by-step explanation:

The volume of a right pyramid is given by the expression = Area of base × height.

Area of base = Area of square at the base

= y × y = y^2.

Now, we substitute these values:

V = y^2 × height

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3 years ago
Given m<12= 121 and m<6= 75, find the measure of each missing angle.
slava [35]

Answer/Step-by-step explanation:

Given:

m<12 = 121°

m<6 = 75°

a. m<1 = m<6 (vertical angles)

m<1 = 75° (substitution)

b. m<12 = m<1 + m2 (alternate exterior angles)

121° = 75° + m<2 (substitution)

121° - 75° = m<2 (subtraction property of equality)

46° = m<2

m<2 = 46°

c. m<1 + m<2 + m<3 = 180° (angles on a straight line)

75° + 46° + m<3 = 180° (substitution)

121° + m<3 = 180°

m<3 = 180° - 121° (subtraction property of equality)

m<3 = 59°

d. m<4 = m<3 (vertical angles)

m<4 = 59° (substitution)

e. m<5 + m<4 + m<6 = 180° (angles on a straight line)

m<5 + 59° + 75° = 180° (substitution)

m<5 + 134° = 180°

m<5 = 180° - 134° (Subtraction property of equality)

m<5 = 46°

f. m<7 = m<12 (vertical angles)

m<7 = 121° (substitution)

g. m<8 = m<4 (vertical angles)

m<8 = 59° (substitution)

h. m<9 = m<6 (Alternate Interior Angles)

m<9 = 75° (substitution)

i. m<10 + m<9 = 180° (Linear Pair)

m<10 + 75° = 180° (substitution)

m<10 = 180° - 75° (Subtraction property of equality)

m<10 = 105°

j. m<11 = m<8 (vertical angles)

m<11 = 59° (substitution)

k. m<13 = m<10 (vertical angles)

m<13 = 105° (substitution)

l. m<14 = m<9 (vertical angles)

m<14 = 75° (substitution)

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3 years ago
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Answer:

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Step-by-step explanation:

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1 year ago
What are they asking?
nadezda [96]
They are asking which one gives both the same answer.
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Can someone please help me on this math problem?!!!
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