Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.


Find the percent of her laps that are completed in less than 134 seconds. (Round your answer to two decimal places.)



The fastest 5% of her laps are under how many seconds? (Round your answer to two decimal places.)

sec

Answer:

97% of her laps are completed in less than 134 seconds.

The fastest 5% of her laps are under 125.96 seconds.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 129.71, \sigma = 2.28[/tex]

Find the percent of her laps that are completed in less than 134 seconds.

We have to find the pvalue of Z when X = 134. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{134 - 129.71}{2.28}[/tex]

[tex]Z = 1.88[/tex]

[tex]Z = 1.88[/tex] has a pvalue of 0.9699, so 97% of her laps are completed in less than 134 seconds.

The fastest 5% of her laps are under how many seconds?

This is the 5th percentile of times, which is X when Z has a pvalue of 0.05, that is, X when Z = -1.645. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.645 = \frac{X - 129.71}{2.28}[/tex]

[tex]X - 129.71 = -1.645*2.28[/tex]

[tex]X = 125.96[/tex]

The fastest 5% of her laps are under 125.96 seconds.

[tex]x1+2x2-x3=3, 2x1+x2-2x3=1, 3x1+4x2-5x3=5[/tex]

6) Sally traveled 352.5 miles on 13 gallons of gas. Set up and solve to proportion to find how many miles she can travel on 18 gallons of gas. Round your answer to the nearest whole number of gallons. Your answer​

mattew drives at an average speed of 62 mph for 5 hours. b
how many miles does mattew drive​

2 1/4 - 1/15














PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEE

can someone give me 500 pts and 5 brainliest

On a coordinate plane, point M is located at (-5, 1) and point N is located at (-5,8).

What is the distance, in units, between point M and point N? Enter the answer in the box.

(5pts) Recall that a standard deck of cards has 52 cards. The cards can be classified according to suits or denominations. There are 4 suits, hearts, diamonds, spades and clubs and there are 13 cards, each of a different denomination, in each suit. The 13 denominations are, Aces, Kings, Queens, ...,Twos, with 4 cards in each denomination (one of each suit). A poker hand consists of a sample of 5 cards drawn from the deck (without replacement). How many poker hands consist of 2 Aces, 2 Kings and a card of a different denomination?

Given the following​ sets, find the set .
U​{​1, ​2, 3, . .​ ., 7​}
A​{​1, 3​, 4​, 5​}
B​{2​, 3​, 5​}
C​{1​, 2​, 3​, 4​, 6​}

Dean picked 28 flowers and Jackie picked 37 flowers. They put the flowers they
picked together. Then, Dean and Jackie divided all of the flowers among 6 flower pots
so that each flower pot had the same number of flowers. How many flowers were left
over after Dean and Jackie had filled the flower pots?

Once Isabel rented the warehouse space, she decided to post ads on several social media sites to advertise her online bookstore. Let x represent the number of months the ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted.

f(x) = 1000(∛x) + 1000

Required:
How many books were sold after 8 months?

Solve this question please

billy jogs 4/5 kilometer every minute.how many kilometers does he jog after 6 1/8 minutes?​

Solve the equation 2x +45 = 9. Explain the steps
and properties you used.

What is 75% of 780?
75% of 780 is

A grocery store sells a bag of 4 oranges for $1.56. How much does one orange cost?

plsss help me solve question 2

2. Ava has 6 boxes of cookies, each box has 30 cookies. Select all the equations that describe the situation. [2 points]
a.ᐧ30=6
b.=6 ᐧ30
c.6=30
d.ᐧ6=30
e.306=

Which institution informs individuals and businesses about their rights and responsibilities?

A.The Federal Trade Commission

B.The Office of the Comptroller

C.The Federal Reserve System

D.The Bureau of Consumer Protection

A baker has 20 pounds of sugar . He uses 3/8 of the sugar to bake cookies . How many pounds does he have left ?

Each school bus going on the field trip holds 36 students and 4 adults. There are 6 field buses on the field trip. How many people are going on the field trip?

Helppppppppppppp meeeeee

Katy ran a mile in 5 minutes. How many seconds are in 5 minutes? Answer without units. *
Captionless Image

I need Help answering this Before 2pm today

What is the answer and steps to the following equation: 6(4-z)=2z

I will give brainiest.

1.3.27
The length of a new rectangular playing field is 8 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 506 yards, what are its dimensions?
The width is

Bea is buying pens and pencils. Pens cost $2 and pencils cost $1. She plans on spending no more than $10 and wants to buy at least 10 items. Which two inequalities model this situation?

What fraction does Point A on the number line below represent?

Find the solution Y=-3x-5 y=9x+7 and show on graph

3 over x plus 6 over y