calculate PART A, PART B, PART C:
PART A: An electronic product takes an average of 3 hours to
move through an assembly line. If the standard deviation of 0.5
hours, what is the probability that an item will take between 1.7
and 3.3 hours to move through the assembly line?
(Round your answer to 3 decimal places.)
PART B: A manufacturer knows that their items have a normally
distributed lifespan, with a mean of 2.5 years, and standard
deviation of 0.7 years.
If 25 items are picked at random, 1% of the time their mean life
will be less than how many years?
Give your answer to one decimal place.
PART C: Delivery times for shipments from a central warehouse
are exponentially distributed with a mean of 2.63 days (note that
times are measured continuously, not just in number of days). A
random sample of 143 shipments are selected and their shipping
times are observed.
Approximate the probability that the average shipping time is less
than 2.29 days.
Enter your answer as a number accurate to 4 decimal places.
A)
for normal distribution z score =(X-μ)/σx | |
here mean= μ= | 3 |
std deviation =σ= | 0.5000 |
probability = | P(1.7<X<3.3) | = | P(-2.6<Z<0.6)= | 0.7257-0.0047= | 0.7210 |
B)
mean μ= | 2.5 |
standard deviation σ= | 0.7000 |
sample size =n= | 25 |
std error=σx̅=σ/√n= | 0.14 |
for 1th percentile critical value of z= | -2.33 | ||
therefore corresponding value=mean+z*std deviation= | 2.2 |
C)
for normal distribution z score =(X-μ)/σ | |
here mean= μ= | 2.63 |
std deviation =σ= | 2.6300 |
sample size =n= | 143 |
std error=σx̅=σ/√n= | 0.2199 |
probability that the average shipping time is less than 2.29 days :
probability = | P(X<2.29) | = | P(Z<-1.55)= | 0.0606 |
calculate PART A, PART B, PART C: PART A: An electronic product takes an average of...
calculate: PART A: Delivery times for shipments from a central warehouse are exponentially distributed with a mean of 2.63 days (note that times are measured continuously, not just in number of days). A random sample of 143 shipments are selected and their shipping times are observed. Approximate the probability that the average shipping time is less than 2.29 days. Enter your answer as a number accurate to 4 decimal places. PART B: A manufacturer knows that their items have a...
An electronic product takes an average of 10 hours to move through an assembly line. If the standard deviation is 0.3 hours, what is the probablity that an 3 hours,what is the probability that an tem will take between 9.5 and 9.7 hours move to move through the assembly line? Assume that the distribution is normal. (Round your answer to 3 decimal places, and report a probability value between 0 and 1.) Answer
Delivery times for shipments from a central warehouse are exponentially distributed with a mean of 2.64 days. A random sample of 81 shipments are selected and their shipping times are observed. Find the probability that the average shipping time is less than 2.28 days.
4. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.4 years, and standard deviation of 3.2 years. If you randomly purchase 21 items, what is the probability that their mean life will be longer than 15 years? (Give answer to 4 decimal places.) 5. A particular fruit's weights are normally distributed, with a mean of 704 grams and a standard deviation of 12 grams. If you pick 12 fruit at random, what is...
An electronic product takes an average of 3.1 hours to move through an assembly line. If the standard deviation is 0.7 hour, what is the probability that an item will take between 3 and 4 hours? Assume the time varies normally. Question 2 options: .673 .0855 .4575 .327
5. A particular fruit's weights are normally distributed, with a mean of 704 grams and a standard deviation of 12 grams. If you pick 12 fruit at random, what is the probability that their mean weight will be between 692 grams and 701 grams (Give answer to 4 decimal places.) 6. A particular fruit's weights are normally distributed, with a mean of 286 grams and a standard deviation of 18 grams. If you pick 25 fruit at random, what is...
A manufacturer knows that their items have a normally distributed length, with a mean of 18 inches, and standard deviation of 5.7 inches. If one item is chosen at random, what is the probability that it is less than 13 inches long? A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.7 years, and standard deviation of 0.7 years. If you randomly purchase one item, what is the probability it will last longer than...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.9 years, and standard deviation of 1 years. If 10 items are picked at random, 4% of the time their mean life will be less than how many years? Give your answer to one decimal place.
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.5 years, and standard deviation of 1 years. If 22 items are picked at random, 1% of the time their mean life will be less than how many years? Give your answer to one decimal place.
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.3 years, and standard deviation of 3 years. If 19 items are picked at random, 6% of the time their mean life will be less than how many years? Give your answer to one decimal place.