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A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the l

Katena32 [7]

Answer:

(a) The fraction of the calls last between 4.50 and 5.30 minutes is 0.3729.

(b) The fraction of the calls last more than 5.30 minutes is 0.1271.

(c) The fraction of the calls last between 5.30 and 6.00 minutes is 0.1109.

(d) The fraction of the calls last between 4.00 and 6.00 minutes is 0.745.

(e) The time is 5.65 minutes.

Step-by-step explanation:

We are given that the mean length of time per call was 4.5 minutes and the standard deviation was 0.70 minutes.

Let X = the length of the calls, in minutes.

So, X ~ Normal( $\mu=4.5,\sigma^{2} =0.70^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean time = 4.5 minutes

$\sigma$ = standard deviation = 0.7 minutes

(a) The fraction of the calls last between 4.50 and 5.30 minutes is given by = P(4.50 min < X < 5.30 min) = P(X < 5.30 min) - P(X $\leq$ 4.50 min)

P(X < 5.30 min) = P( $\frac{X-\mu}{\sigma}$ < $\frac{5.30-4.5}{0.7}$ ) = P(Z < 1.14) = 0.8729

P(X $\leq$ 4.50 min) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{4.5-4.5}{0.7}$ ) = P(Z $\leq$ 0) = 0.50

The above probability is calculated by looking at the value of x = 1.14 and x = 0 in the z table which has an area of 0.8729 and 0.50 respectively.

Therefore, P(4.50 min < X < 5.30 min) = 0.8729 - 0.50 = 0.3729.

(b) The fraction of the calls last more than 5.30 minutes is given by = P(X > 5.30 minutes)

P(X > 5.30 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{5.30-4.5}{0.7}$ ) = P(Z > 1.14) = 1 - P(Z $\leq$ 1.14)

= 1 - 0.8729 = 0.1271

The above probability is calculated by looking at the value of x = 1.14 in the z table which has an area of 0.8729.

(c) The fraction of the calls last between 5.30 and 6.00 minutes is given by = P(5.30 min < X < 6.00 min) = P(X < 6.00 min) - P(X $\leq$ 5.30 min)

P(X < 6.00 min) = P( $\frac{X-\mu}{\sigma}$ < $\frac{6-4.5}{0.7}$ ) = P(Z < 2.14) = 0.9838

P(X $\leq$ 5.30 min) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{5.30-4.5}{0.7}$ ) = P(Z $\leq$ 1.14) = 0.8729

The above probability is calculated by looking at the value of x = 2.14 and x = 1.14 in the z table which has an area of 0.9838 and 0.8729 respectively.

Therefore, P(4.50 min < X < 5.30 min) = 0.9838 - 0.8729 = 0.1109.

(d) The fraction of the calls last between 4.00 and 6.00 minutes is given by = P(4.00 min < X < 6.00 min) = P(X < 6.00 min) - P(X $\leq$ 4.00 min)

P(X < 6.00 min) = P( $\frac{X-\mu}{\sigma}$ < $\frac{6-4.5}{0.7}$ ) = P(Z < 2.14) = 0.9838

P(X $\leq$ 4.00 min) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{4.0-4.5}{0.7}$ ) = P(Z $\leq$ -0.71) = 1 - P(Z < 0.71)

= 1 - 0.7612 = 0.2388

The above probability is calculated by looking at the value of x = 2.14 and x = 0.71 in the z table which has an area of 0.9838 and 0.7612 respectively.

Therefore, P(4.50 min < X < 5.30 min) = 0.9838 - 0.2388 = 0.745.

(e) We have to find the time that represents the length of the longest (in duration) 5 percent of the calls, that means;

P(X > x) = 0.05 {where x is the required time}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-4.5}{0.7}$ ) = 0.05

P(Z > $\frac{x-4.5}{0.7}$ ) = 0.05

Now, in the z table the critical value of x which represents the top 5% of the area is given as 1.645, that is;

$\frac{x-4.5}{0.7}=1.645$

${x-4.5}{}=1.645 \times 0.7$

x = 4.5 + 1.15 = 5.65 minutes.

SO, the time is 5.65 minutes.

7 0

4 years ago

You deposit $1,600 in a bank account. The account pays 3% annual Interest compounded monthly. Find the balance after 5 years

kumpel [21]

Step-by-step explanation:

step 1. let's call the amount of money A, the initial amount P, the yearly rate r, the number of compounds per year n.

step 2. A = P(1 + r/n)^(nt)

step 3. A = 1600(1 + .03/12)^((12)(5)

step 4. A = 1600(1.0025)^(60)

step 5. A = $1858.59

8 0

3 years ago

3 ^(1 − 7 x = 7 ^x find the exact value

Shalnov [3]

Answer:

x

=

ln

(

3

)

7

ln

(

3

)

+

ln

(

7

)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

-2/5x+6=8 can you help me

ale4655 [162]

If you would like to solve the equation - 2/5 * x + 6 = 8, you can do this using the following steps:

- 2/5 * x + 6 = 8
- 2/5 * x = 8 - 6
- 2/5 * x = 2 /*(-5/2)
x = 2 * (- 5/2)
x = - 5

The correct result would be -5.

7 0

3 years ago

Read 2 more answers

Regina, Phil, and Joseph each wrote expressions to represent their hourly earnings for an after-school job where h represents th

Vladimir79 [104]

Answer:

Disagree

On weeks when Joseph works extra 2/3 hours more than Phil, Phil and Joseph can earn the same amount of money

Step-by-step explanation:

The given expression for the hourly earnings of Regina, Phil and Joseph are as follows;

Regina: 6.50·h + 16

Phil: 3·(2.5·H + 5)

Joseph: 7.50·h + 10

The number of hours worked = h

The hourly earnings for Phil equated to the hourly earnings of Joseph gives;

3·(2.5·H + 5) = 7.50·h + 10

Simplifying we get;

3 × 2.5·h + 3 × 5 = 7.50·h + 10

7.5·h + 15 = 7.50·h + 10

Which gives

15 = 10 + 5 = 10 which is not correct.

Therefore, when both Phil and Joseph works the same number of hours, in the week, Phil will earn 5 units more Joseph

However, we have that, where Joseph works extra 5/7.5 or 2/3 hours more than Phil, every week, they will earn the same amount of money every week.

Therefore, it is possible for Phil and Joseph to earn the same amount of money when Joseph works extra 2/3 hours more than Phil which gives;

On weeks when Joseph works extra 2/3 hours more than Phil, Phil and Joseph can earn the same amount of money.

3 0

3 years ago