Mathematics : asked on neash31
 11.06.2022

Mr. Wilcox spends a full day at Gingerman Raceway testing some new tires on his Honda
Civic. For 400 laps, he records his laptime in minutes. At the end of the day, he plots the
distribution of times and realizes that it follows an approximately normal distribution with
a mean of 1.84 and a standard deviation of 0.07.
1. Label the values 1, 2, and 3 standard deviations above and below the mean.
05D
-1 5D
1 SD
-2 SD
2 SD
-3 SD
3 SD
2. What percentage of the laptimes are less than 1.70 minutes?
3. What percentage of the laptimes are greater than 1.77 minutes?
4. What percentage of the laptimes are between 1.70 and 1.91 minutes?
5. What laptime would be in the slowest 2.5% of all laptimes?

. 40

Faq

StudenGPT
Step-by-step answer
P Answered by Studen AI
To find the proportion of laps within the desired range of laptimes, we need to calculate the z-scores for the lower and upper bounds and then find the area under the normal distribution curve between those z-scores.

Step 1: Calculate the z-scores
The z-score formula is given by: z = (x - μ) / σ

For the lower bound of 1.75 minutes:
z1 = (1.75 - 1.84) / 0.07 = -1.29

For the upper bound of 1.85 minutes:
z2 = (1.85 - 1.84) / 0.07 = 0.14

Step 2: Use z-scores to find the proportion
Using a standard normal distribution table or a calculator, we can find the proportion of values between the z-scores of -1.29 and 0.14.

Let's denote this proportion as P(z1 < Z < z2).

P(z1 < Z < z2) = P(Z < z2) - P(Z < z1)

From the standard normal distribution table (or calculator), we find:
P(Z < z2) = 0.5564
P(Z < z1) = 0.0985

Substituting the values into the formula:
P(z1 < Z < z2) = 0.5564 - 0.0985 = 0.4579

Therefore, approximately 45.79% of Mr. Wilcox's laps were within the desired range of 1.75 to 1.85 minutes.

Interpretation:
This means that from the recorded 400 laps, around 45.79% of them had laptimes between 1.75 and 1.85 minutes. Mr. Wilcox achieved his goal of consistently maintaining laptimes within this range for a significant portion of his laps.
Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
Step-by-step answer
P Answered by PhD

Given height of gymnasium is 5/6 height of 30 foot ball

therefore height of gymnasium=5/6 * 30

=25 feet

Try asking the Studen AI a question.

It will provide an instant answer!

FREE