Mathematics, 18.02.2020 20:09, kaydencool1234

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch and a standard deviation of 0.0004 inch. A. What is the probability that the diameter of a dot exceeds 0.0026 inch? B. What is the probability that a diameter is between 0.0014 and 0.0026? C. What standard deviation of diameters is needed so that the probability in part (b) is 0.995?

Answers: 3

Show answers

Answers

answered: kuadirkennedy

(a) 0.06681

(b) 0.86638

Step-by-step explanation:

We are given that the diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch and a standard deviation of 0.0004 inch i.e.; $\mu$ = 0.002 inch and $\sigma$ = 0.0004

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

(a) Let X = diameter of a dot

P(X > 0.0026 inch) = P( $\frac{X -\mu}{\sigma}$ > $\frac{0.0026 -0.002}{0.0004}$ ) = P(Z > 1.5) = 1 - P(Z <= 1.5)

= 1 - 0.93319 = 0.06681

(b) P(0.0014 < X < 0.0026) = P(X < 0.0026) - P(X <= 0.0014)

P(X < 0.0026) = P( $\frac{X -\mu}{\sigma}$ < $\frac{0.0026 -0.002}{0.0004}$ ) = P(Z < 1.5) = 0.93319

P(X <= 0.0014) = P( $\frac{X -\mu}{\sigma}$ <= $\frac{0.0014 -0.002}{0.0004}$ ) = P(Z <= -1.5) = 1 - P(Z <= 1.5)

= 1 - 0.93319 = 0.06681

Therefore, P(0.0014 < X < 0.0026) = 0.93319 - 0.06681 = 0.86638 .

P( $\frac{0.0014 -0.002}{\sigma}$ < $\frac{X -\mu}{\sigma}$ < $\frac{0.0026 -0.002}{\sigma}$ ) = 0.995

P( $\frac{ -0.0006}{\sigma}$ < Z < $\frac{0.0006}{\sigma}$ ) = 0.995

P(Z < $\frac{0.0006}{\sigma}$ ) - P(Z <= $\frac{-0.0006}{\sigma}$ ) = 0.995

P(Z < $\frac{0.0006}{\sigma}$ ) - (1 - P(Z < $\frac{0.0006}{\sigma}$ ) ) = 0.995

2 * P(Z < $\frac{0.0006}{\sigma}$ ) - 1 = 0.995

P(Z < $\frac{0.0006}{\sigma}$ ) = 0.9975

On seeing the z table we observe that at critical value of x = 2.81 we get the probability area of 0.9975 i.e.;

$\frac{0.0006}{\sigma}$ = 2.81 ⇒ $\sigma$ = 0.000214

Therefore, 0.000214 standard deviation of diameters is needed so that the probability in part (b) is 0.995 .

answered: Guest

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft 60 sec 60 min 158400 ft

* * =

1 sec 1 min 1 hour hour

we know that there are 5280 ft per mile

158400 ft 1 mile 30 miles

* =

1 hour 5280 ft 1 hour

so in 1 hour it can travel 30 miles

answered: Guest

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 19:00, glowbaby123

Tabby sells clothing at a retail store, and she earns a commission of 6.25% on all items she sells. last week she sold a pair of jeans for $32.50, a skirt for $18.95, and 2 blouses for $14.95 each. what was tabby's total commission? a $4.15 b $5.08 c $81.35 d $348.60

Answers: 3

continue

Mathematics, 21.06.2019 20:00, cferguson

Someone answer asap for ! the total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?

Answers: 1

continue

Mathematics, 21.06.2019 21:00, OceanClaws

The area of a rectangle is 10 cm^2. one side of the rectangle is x cm. express the perimeter of the rectangle in terms of x and show that this rectangle cannot have a perimeter of 12 cm. the perimeter of the rectangle in terms of x is __ cm

Answers: 1

continue

Mathematics, 21.06.2019 23:00, krystinayagel013

Math i have no idea how to do a and b

Answers: 2

continue

Do you know the correct answer?

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002...