1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
IrinaK [193]
3 years ago
14

The life times of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 h

ours. The population distribution is normal. Suppose that you purchase nine bulbs, which can be regarded as a random sample from the manufacturer’s output.
a) What is the mean of the sample mean lifetime?
b) What is the variance of the sample mean?
c) What is the standard error of the sample mean?
d) What is the probability that, on average, those ninelightbulbs have lives of fewer than 1,050 hours?
Mathematics
1 answer:
Nezavi [6.7K]3 years ago
8 0

Answer:

a. 1200hours

b.  σ² = 400² =160000hour

c. standard error = 133.33

d. for 9 lightbulb it is likely that 9*0.146 = 1.31 bulbs will have lives of fewer than 1,050 hours?

Step-by-step explanation:

mean of 1,200 hours

σ, a standard deviation of 400 hours.

Sample size, N =  nine bulbs,

a) mean of the sample mean lifetime: is given as 1,200 hours

b) variance of the sample mean is the square of the  σ, a standard deviation of 400 hours.

σ² = 400² =160000hours

c) What is the standard error of the sample mean?

The standard deviation of a sampling distribution of mean values is called the standard error of the means,

standard error of the means,  σx = σ √N

The formula for the standard error of the means is true for all values infinite number of sample, N.

σx = σ √N

     =400  √9 = 400/3 =133.3333

d) the probability that, on average, those nine lightbulbs have lives of fewer than 1,050 hours

The area under part of a normal probability curve is  directly proportional to probability and the value is calculated as

z = ( x₁−x) /σ

where z = propability of normal curve

x₁ = variate mean = 1050hours

x = mean of 1200hours

σ = standard deviation = 400

applying the formula,

z= (1050-1200)/400

z = 150/400 =0.375

Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 0.375 corresponds to an area of 0.1460 between the mean value.

Thus the probability of a lightbulbs having lives of fewer than 1,050 hours is 0.1460.

for 9 lightbulb it is likely that 9*0.146 i.e. 1.31 bulbs will have lives of fewer than 1,050 hours?  

You might be interested in
In problems like -20≤5y, when you divide by 5 do you reverse the symbol because -20 is negative?
vampirchik [111]
No, you only reverse the symbol when the divisor is negative
8 0
3 years ago
Read 2 more answers
Which ordered pair is a solution of the equation y = 4x? (1, 3) (-1, -4) (-4, -1) (1, -4)
Sphinxa [80]
(-4,-1) because -1 × 4= -4 and -4=y
4 0
3 years ago
Which of the following is defined as the number of square units needed to fill it? Region
Artemon [7]
I'm 90% sure it's Area.
6 0
2 years ago
Read 2 more answers
What are the prime factorazations for the numbers <br> 66<br> 55<br> 88<br> 99?
ra1l [238]

Answer:

999 because it it an sum it it

6 0
2 years ago
Helpppp plzzzzzzzzzzzzz
Kay [80]

Answer:

x=90 possibly

Step-by-step explanation:

3x all at 30 degrees. but not posative so please check elsewhere.

4 0
2 years ago
Other questions:
  • Which equation could be used to find the length of the hypotenuse?
    9·2 answers
  • What is 3 division 68 and show your work plz
    7·2 answers
  • You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distrib
    10·1 answer
  • A single microvillus is a rod-like structure that is 1.0 μm in height. it has a hemispherical top approximately 0.1 μm in diamet
    9·1 answer
  • Ma poate ajuta cineva pls!
    5·1 answer
  • Plz help very important
    10·1 answer
  • The following examples illustrate the inverse property of multiplication. Study the examples, then choose the statement that bes
    9·2 answers
  • Find 6A-8B (picture provided)
    14·1 answer
  • 30% in simplest form
    9·2 answers
  • A loan used for buying a home is called a mortgage. The Fortunato family is borrowing $430,000 to buy a home. They are taking ou
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!