Question 1

Your company issues flight insurance. You charge $2 and in the event of a plane crash, you will pay out $1 million to the victim or his or her family. In 1989, the probability of a plane crashing on a single trip was 0.00000165. If ten people per flight buy insurance from you, what was your approximate probability of losing money over the course of 110 million flights in 1989  Round your answer to four decimal places. [Hint: First determine how many crashes there must be for you to lose money.]

Accepted Answer

The answer of Your company issues flight insurance. You charge...

Question 2

The mean batting average in major league baseball is about 0.250. Supposing that batting averages are normally distributed, that the standard deviation in the averages is 0.05, and that there are 250 batters, what is the expected number of batters with an average of at least 0.400  Round your answer to two decimal places.
?
The answer is __________ batters.

Accepted Answer

The answer of The mean batting average in major league...

Question 3

Suppose X is a normal random variable with $\mu = 370$ and $\sigma = 60$ . Find the value, rounding to four decimal places, of
​ $P ( 430 \leq X \leq 460 ) =$ __________

Accepted Answer

The answer of Suppose X is a normal random variable...

Question 4

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 80 crashes. Round your answer to four decimal places. Round Z to two decimal places.

Accepted Answer

The answer of The probability of a plane crashing on...

Question 5

Z is the standard normal distribution. Find the probability $P ( - 2.23 \leq Z \leq 1.43 )$ . Please, round your answer to three decimal places.
​ $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

Accepted Answer

The answer of Z is the standard normal distribution. Find...

Question 6

Compute the standard deviation of the data sample.  
 $- 4,3,6,9,14$  
Round your answer to two decimal places if necessary.

Accepted Answer

The standard deviation is calculated by first finding the mean of the data, then calculating the squared differences from the mean, averaging those, and finally taking the square root. For the data $-4, 3, 6, 9, 14$, the mean is $5.6$. The squared differences from the mean are $92.16, 6.76, 0.16, 11.56, 70.56$, respectively. The average of these squared differences is $36.24$, and the square root of $36.24$ is approximately $6.02$, which is rounded to $6.02$ when rounded to two decimal places.

Question 7

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) Assuming that the time it takes a student to complete each task is independent of the others, find the probability that a student will take at least 10 minutes to complete each of Tasks 1 and 2. Round your answer to four decimal places. $$\begin{array} { | l | l | l | } 
\hline \text { Task } & \begin{array} { l } 
\text { Mean Time } \
\text { (minutes) }
\end{array} & \begin{array} { l } 
\text { Standard } \
\text { Deviation }
\end{array} \
\hline \text { Task 1: Descriptive Analysis of Data } & 12.5 & 6.0 \
\hline \text { Task 2: Standardizing Scores } & 11.9 & 9.0 \
\hline \text { Task 3: Poison Probability Table } & 7.3 & 3.9 \
\hline \text { Task 4:Areas Under Normal Curve } & 9.1 & 5.5 \
\hline
\end{array}$$

Accepted Answer

The answer of This exercise is based on the following...

Question 8

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to three decimal places.

Accepted Answer

The answer of Find the probability that a normal variable...

Question 9

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score 340 or lower. Round your answer to four decimal places.

Accepted Answer

The answer of LSAT test scores are normally distributed with...

Question 10

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) It can be shown that if X and Y are independent normal random variables with means $\mu _ { X }$ and $\mu _ { y }$ and standard deviations $\sigma _ { X }$ and $\sigma _ { y }$ respectively, then their sum $X + Y$ is also normally distributed and has mean $\mu = \mu _ { X } + \mu _ { Y }$ and standard deviation $\sigma = \sqrt { \sigma ^ { 2 } X + \sigma ^ { 2 } Y }$ . Assuming that the time it takes a student to complete each task is independent of the others, find the probability that a student will take at least 20 minutes to complete both Tasks 3 and 4. Round your answer to four decimal places. Round Z to two decimal places. $$\begin{array} { | l | l | l | } 
\hline \text { Task } & \begin{array} { l } 
\text { Mean Time } \
( \text { minutes } )
\end{array} & \begin{array} { l } 
\text { Standard } \
\text { Deviation }
\end{array} \
\hline \text { Task 1: Descriptive Analysis of Data } & 11.4 & 5.0 \
\hline \text { Task 2: Standardizing Scores } & 11.9 & 9.0 \
\hline \text { Task 3: Poisson Probability Table } & 7.3 & 3.9 \
\hline \text { Task 4: Areas Under Normal Curve } & 9.1 & 5.5 \
\hline
\end{array}$$

Accepted Answer

The answer of This exercise is based on the following...

Question 11

Suppose X is a normal random variable with $\mu = 50$ and $\sigma = 5$ . Find the value, rounding to four decimal places, of
​ $P ( 49 \leq X \leq 58 ) =$ __________

Accepted Answer

The answer of Suppose X is a normal random variable...

Question 12

IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. Find the approximate number of people in the U.S. (assuming a total population of 280,000,000) with an IQ higher than 120.
​
Round your answer to the nearest 100,000.
​
__________ people

Accepted Answer

The answer of IQ scores (as measured by the Stanford-Binet...

Question 13

X has a normal distribution with the given mean and standard deviation. Find the probability. Please, round the answer to three decimal places.
​ $\mu = 40$ , $\sigma = 5$ ​ $P ( 23 \leq X \leq 44 ) \approx$ __________

Accepted Answer

The answer of X has a normal distribution with the...

Question 14

The population standard deviation is greater than the sample standard deviation.

Accepted Answer

This is a possibility, but not always true. It depends on the specific data set and the size of the sample. In general, the larger the sample size, the closer the sample standard deviation will be to the population standard deviation.

Question 15

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve.
​  ​
Round your answer to four decimal places.
​ $P ( 0.6 \leq Z \leq 1.88 ) =$ __________

Accepted Answer

The answer of Find the value of the probability of...

Question 16

If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of U.S. households had an income of $50,000 or more  Express your answer to the nearest 1%. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \
\hline \begin{array} { l } 
\text { Mean } \
\text { household } \
\text { income }
\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \
\hline \begin{array} { l } 
\text { Standard } \
\text { deviation }
\end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \
\hline
\end{array}$$  
__________% of households

Accepted Answer

The answer of If we model after-tax household income with...

Question 17

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising  (Assume that the times between failures are normally distributed.)

Accepted Answer

The answer of The new computer your business bought lists...

Question 18

If you roll a die 300 times, what is the probability that you will roll between 50 and 80 sixs  Please, round your answer to three decimal places.

Accepted Answer

The answer of If you roll a die 300 times,...

Question 19

If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of German households are either very wealthy (income at least $100,000) or very poor (income at most $12,000)  Express your answer to the nearest 1%. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \
\hline \begin{array} { l } 
\text { Mean } \
\text { household } \
\text { income }
\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \
\hline \begin{array} { l } 
\text { Standard } \
\text { deviation }
\end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \
\hline
\end{array}$$  
__________% of households

Accepted Answer

The answer of If we model after-tax household income with...

Question 20

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 350 and 550. Round your answer to four decimal places.

Accepted Answer

The answer of LSAT test scores are normally distributed with...

Quiz 9: Random Variables and Statistics

Suppose X is a normal random variable with $\mu = 370$ and $\sigma = 60$ . Find the value, rounding to four decimal places, of $P ( 430 \leq X \leq 460 ) =$ __________

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 80 crashes. Round your answer to four decimal places. Round Z to two decimal places.

Z is the standard normal distribution. Find the probability $P ( - 2.23 \leq Z \leq 1.43 )$ . Please, round your answer to three decimal places. $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

Compute the standard deviation of the data sample. $- 4,3,6,9,14$ Round your answer to two decimal places if necessary.

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to three decimal places.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score 340 or lower. Round your answer to four decimal places.

Suppose X is a normal random variable with $\mu = 50$ and $\sigma = 5$ . Find the value, rounding to four decimal places, of $P ( 49 \leq X \leq 58 ) =$ __________

X has a normal distribution with the given mean and standard deviation. Find the probability. Please, round the answer to three decimal places. $\mu = 40$ , $\sigma = 5$ $P ( 23 \leq X \leq 44 ) \approx$ __________

The population standard deviation is greater than the sample standard deviation.

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising (Assume that the times between failures are normally distributed.)

If you roll a die 300 times, what is the probability that you will roll between 50 and 80 sixs Please, round your answer to three decimal places.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 350 and 550. Round your answer to four decimal places.

Quiz 9: Random Variables and Statistics

Suppose X is a normal random variable with μ=370\mu = 370μ=370 and σ=60\sigma = 60σ=60 . Find the value, rounding to four decimal places, of ​ P(430≤X≤460)=P ( 430 \leq X \leq 460 ) =P(430≤X≤460)= __________

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 80 crashes. Round your answer to four decimal places. Round Z to two decimal places.

Z is the standard normal distribution. Find the probability P(−2.23≤Z≤1.43)P ( - 2.23 \leq Z \leq 1.43 )P(−2.23≤Z≤1.43) . Please, round your answer to three decimal places. ​ P(−2.23≤Z≤1.43)≈P ( - 2.23 \leq Z \leq 1.43 ) \approxP(−2.23≤Z≤1.43)≈ __________

Compute the standard deviation of the data sample. −4,3,6,9,14- 4,3,6,9,14−4,3,6,9,14 Round your answer to two decimal places if necessary.

Find the probability that a normal variable takes values more than 14\frac { 1 } { 4 }41​ standard deviations away from its mean. Please, round the answer to three decimal places.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score 340 or lower. Round your answer to four decimal places.

Suppose X is a normal random variable with μ=50\mu = 50μ=50 and σ=5\sigma = 5σ=5 . Find the value, rounding to four decimal places, of ​ P(49≤X≤58)=P ( 49 \leq X \leq 58 ) =P(49≤X≤58)= __________

X has a normal distribution with the given mean and standard deviation. Find the probability. Please, round the answer to three decimal places. ​ μ=40\mu = 40μ=40 , σ=5\sigma = 5σ=5 ​ P(23≤X≤44)≈P ( 23 \leq X \leq 44 ) \approxP(23≤X≤44)≈ __________

The population standard deviation is greater than the sample standard deviation.

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. ​ ​ Round your answer to four decimal places. ​ P(0.6≤Z≤1.88)=P ( 0.6 \leq Z \leq 1.88 ) =P(0.6≤Z≤1.88)= __________

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising (Assume that the times between failures are normally distributed.)

If you roll a die 300 times, what is the probability that you will roll between 50 and 80 sixs Please, round your answer to three decimal places.

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 350 and 550. Round your answer to four decimal places.

Suppose X is a normal random variable with $\mu = 370$ and $\sigma = 60$ . Find the value, rounding to four decimal places, of $P ( 430 \leq X \leq 460 ) =$ __________

Z is the standard normal distribution. Find the probability $P ( - 2.23 \leq Z \leq 1.43 )$ . Please, round your answer to three decimal places. $P ( - 2.23 \leq Z \leq 1.43 ) \approx$ __________

Compute the standard deviation of the data sample. $- 4,3,6,9,14$ Round your answer to two decimal places if necessary.

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to three decimal places.

Suppose X is a normal random variable with $\mu = 50$ and $\sigma = 5$ . Find the value, rounding to four decimal places, of $P ( 49 \leq X \leq 58 ) =$ __________

X has a normal distribution with the given mean and standard deviation. Find the probability. Please, round the answer to three decimal places. $\mu = 40$ , $\sigma = 5$ $P ( 23 \leq X \leq 44 ) \approx$ __________