The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of

Answer and Explanation:

We have:

Population mean,

μ

=

3

,

000

hours

Population standard deviation,

σ

=

696

hours

Sample size,

n

=

36

1) The standard deviation of the sampling distribution:

σ

¯

x

=

σ

√

n

=

696

√

36

=

116

2) As per the central limit theorem, the expected value of the sampling distribution is equal to the population mean.

Therefore:

The expected value of the sampling distribution is equal to the population mean,

μ

¯

x

=

μ

=

3

,

000

The standard deviation of the sampling distribution,

σ

¯

x

=

116

The shape of the sampling distribution of

¯

x

is approximately normal. As the sample size is more than

30

.

3) The probability that the average life in the sample will be between

2670.56

and

2809.76

hours:

P

(

2670.56

<

x

<

2809.76

)

=

P

(

2670.56

−

3000

116

<

z

<

2809.76

−

3000

116

)

=

P

(

−

2.84

<

z

<

−

1.64

)

=

P

(

z

<

−

1.64

)

−

P

(

z

<

−

2.84

)

=

0.0482

Using Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)

4) The probability that the average life in the sample will be greater than

3219.24

hours:

P

(

x

>

3219.24

)

=

P

(

z

>

3219.24

−

3000

116

)

=

P

(

z

>

1.89

)

=

0.0294

Using Excel: =NORMSDIST(-1.89)

5) The probability that the average life in the sample will be less than

3180.96

hours:

P

(

x

<

3180.96

)

=

P

(

z

<

3180.96

−

3000

116

)

=

P

(

z

<

1.56

)

=

0.9406

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is