Homework Questions
5.3
- A distribution of values is normal with a mean of 1493.5 and a standard deviation of 45.7
Find the probability that a randomly selected value is less than 1528.7
P (X < 1528.7) =0.7794-0.5
- A distribution of values is normal with a mean of 822.2 and a standard deviation of 45.1
Find the probability that a randomly selected value is greater than 935.44
P (X > 935.4) =0.9945
- A distribution of values is normal with a mean of 684.5 and a standard deviation of 27.5
Find the probability that a randomly selected value is between 643.8 and 700.2
P(x>643.8)=0.0694
P(x>700.2)=0.7088
P (643.8 < X < 700.2) =0.7088-0.0694
=0.6394
The number of miles a certain type of brake pad will last is normally distributed with a mean of 56000 miles and standard deviation 2590 miles. Find the probability that, if you install this type of brake pad, it will last more than 59315 miles.
(From zscore table)
P(X> 59315) =1-0.8997
=0.1003
- The heights of women aged 20-29 are normally distributed with mean 65.7 inches and standard deviation 3.3 inches. What percent of women are below 59.7 inches? Round to the nearest hundredth of a percent.
P(x<59.7) =0.0344
Percentage of women below 59.7 inches
=0.0344*100
- Statista reported in 2014 that the mean number of Facebook friend for 18 to 24 year olds was 649. Assuming the distribution is normal with mean 649 friends and standard deviation 120 friends, what is the probability that a randomly selected 18 to 24 year old will have between 435 and 985 friends?
1.78
P (435< X < 985) = 0.9981-0.0375
=0.9606
- Suppose that a brand of light bulb lasts on average 2628 hours with a standard deviation of 138 hours. Assume the life of the light bulb is normally distributed. Calculate the probability that a particular bulb will last from 2191 to 3064 hours?
P(2191< X <3064) =0.9992-0.0008
=0.9984
- Suppose a drive for a PGA Tour golfer is 316.93 yards with a standard deviation of 16.5 yards. Find the probability that a random drive will travel more than 317.9 yards.
P(X> 317.9) = 1-0.5239
=0.4761
- Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0 degree Celsius and a standard deviation of 1.00 degree Celsius.
A single thermometer is randomly selected and tested. Let X represent the reading of this thermometer at freezing. What reading separates the highest 33.36% from the rest?
Here we need to find x such that
P(X>x)=0.10
So, x=1.282
Hence we will find X using z-formula
Since the mean is 0 and standard deviation is 1
X=-1.282
We then need to find a value C such that
P(x<C) =0.3336
0.5+P (0<x<c) =0.3336-0.5
=-0.1336
Using z-table we find
P(0<x<-0.43)
c= -0.43 degree Celsius
6.1/6.2 Homework
- Random samples of size 47 are drawn from a population with mean 138.4 and standard deviation 18.3. Find the mean and the standard deviation of the sample mean. Round to four decimal places.
Sample size, n=47
Since mean is unbiased estimator of population mean i.e.
Meaning =138.4
Therefore,
=N (138.4, 48.8487)
Sample mean=138.4
Standard deviation=48.8487
- Random samples of size 102 are drawn from a population with mean 97.7 and standard deviation 19.4. Find the mean and the standard deviation of the sample mean. Round to four decimal places.
Therefore,
=N (97.7, 37.2652)
Sample mean=97.7
Standard deviation=37.2652
- A population is normally distributed with mean 23.9 and standard deviation 3.6. Find the probability that a sample of 9 values taken from this population will have a mean less than 24.
- A manufacturer knows that their items have a normally distributed length, with a mean of 18 inches, and standard deviation of 3.6 inches.
If 25 items are chosen at random, what is the probability that their mean length is less than 18.4 inches?
- A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.9 years, and standard deviation of 0.6 years.
If you randomly purchase 16 items, what is the probability that their mean life will be longer than 14 years?
- A particular fruit’s weights are normally distributed, with a mean of 262 grams and a standard deviation of 30 grams.
If you pick 16 fruit at random, what is the probability that their mean weight will be between 240 grams and 253 grams
- The average GPA at a college is 3.03 with a standard deviation of 0.5
If 42 students are selected at random, what is the probability that their average GPA will be between 2.76 and 3.2?
- From 1985 to 2006, the average height of an NBA player was 6 foot 7(79 inches). Suppose the distribution is approximately normal and the standard deviation is 1.5 inches. What is the probability that, of 39 NBA players selected at random, their average height is more than 79 inches?
- IQ scores are normally distributed with a mean of 98 and standard deviation of 5. In a sample of 41 people, what is the probability that their average IQ sore does not differ from the mean by more than two points?
- Mathematics majors generally have one of the highest starting salaries. Suppose the average starting salary for mathematics majors is $45000 with a standard deviation of $3600. Find the probability that 33 mathematics majors have an average starting salary less than $45795 thousand.
=0.9015
