5. The length of similar components produced by a company are approximated by a normal distribution model with a mean of 5 cm and a standard deviation of 0.02 cm. If a component is chosen at random a) what is the probability that the length of this component is between 4.98 and 5.02 cm

the probability that  he length of this component is between 4.98 and 5.02 cm is 0.682 (68.2%)

Step-by-step explanation:

Since the random variable X= length of component chosen at random , is normally distributed, we can define the following standardized normal variable Z:

Z= (X- μ)/σ

where μ= mean of X  , σ= standard deviation of X

for a length between 4.98 cm and 5.02 cm , then

Z₁= (X₁- μ)/σ =  (4.98 cm - 5 cm)/0.02 cm = -1

Z₂= (X₂- μ)/σ = (5.02 cm - 5 cm)/0.02 cm = 1

therefore the probability that the length is between 4.98 cm and 5.02 cm is

P( 4.98 cm ≤X≤5.02 cm)=P( -1 ≤Z≤ 1) = P(Z≤1) - P(Z≤-1)

from standard normal distribution tables we find that

P( 4.98 cm ≤X≤5.02 cm) = P(Z≤1) - P(Z≤-1) = 0.841 - 0.159 = 0.682 (68.2%)

therefore the probability that  he length of this component is between 4.98 and 5.02 cm is 0.682 (68.2%)

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1