Question

In: Statistics and Probability

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3...

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3 years, and standard deviation of 0.6 years.

If you randomly purchase 17 items, what is the probability that their mean life will be longer than 3 years?

Solutions

Expert Solution

Solution :

Given that,

mean = = 3

standard deviation = =0.6

n=17

= =3

= / n =0.6 / 17 = 0.1455

P( > 3) = 1 - P( < 3)

= 1 - P[( - ) / < (3-3) /0.1455 ]

= 1 - P(z <0 )

Using z table

= 1 - 0.5

= 0.5

probability= 0.5

orchestra answered 3 years ago
Next > < Previous

Related Solutions

A.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of...
A.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of 1 years. If you randomly purchase one item, what is the probability it will last longer than 9 years? B.) A particular fruit's weights are normally distributed, with a mean of 784 grams and a standard deviation of 24 grams. If you pick one fruit at random, what is the probability that it will weigh between 845 grams...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7 years, and standard deviation of 1.6 years. If you randomly purchase one item, what is the probability it will last longer than 11 years?
1. A manufacturer knows that their items have a normally distributed lifespan, with a mean of...
1. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14.1 years, and standard deviation of 2.8 years. If you randomly purchase one item, what is the probability it will last longer than 20 years? 2. A particular fruit's weights are normally distributed, with a mean of 506 grams and a standard deviation of 21 grams. If you pick one fruit at random, what is the probability that it will weigh between 475 grams...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.7...
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 6 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 10...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10 years, and standard deviation of 1.8 years. If 20 items are picked at random, 2% 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 7.4...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.4 years, and standard deviation of 0.6 years. If 13 items are picked at random, 8% 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 12...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12 years, and standard deviation of 0.5 years. If 5 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 12...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12 years, and standard deviation of 0.5 years. If 5 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 10.3...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.3 years, and standard deviation of 2.4 years. If you randomly purchase 21 items, what is the probability that their mean life will be longer than 11 years? (Give answer to 4 decimal places.)
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.7...
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.7 years, and standard deviation of 1.1 years. Round all answers to 3 decimals. (a) If you randomly purchase one item, what is the probability it will last longer than 4 years? Show your work. Show me what you entered into the calculator. (b) If you randomly select one item, what is the probability it will last less than 5 years? Show your work. Show...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT