Question

The weight of a certain type of ﬁshes follows a normal distribution with mean 250 grams and standard deviation 20 grams.

(a) Find the probability that the weight of a ﬁsh will be less than
260 grams.

(b) Find the probability that the weight of a ﬁsh will exceed 245
grams.

(c) Find the probability that the weight of a ﬁsh will be from 200
to 270 grams.

(d) Find the weight of the ﬁsh that exceeds 90% of the weights.

Answer #1

Let X be weight of the fish

X ~ Normal (250 , 20)

a) P( X < 260) = P( < )

= P( z < 0.5)

= 0.69146

b) P( X > 245) = P( > )

= P( z > -0.25)

= P( z < 0.25)

= 0.59871

c) P( 200 < X < 270) = P( < > )

= P( -2.5 < z <1 )

= P( z < 1) - P( z < -2.5)

= P( z < 1) - 1 + P(z < 2.5)

= 0.84134 - 1 + 0.99379

= **0.83513**

d) We need to find the 90th percentile

P( Z < z) = 0.9

P( Z < 1.282) =0.9

z = 1.282

= 1.282

= 1.282

X= 250 + 20*1.282

**X= 275.64**

The lifetime of a certain battery follows a normal distribution
with a mean 276 minutes and standard deviation 20 minutes. We took
a random sample of 100 of these batteries. What is the probability
that the sample mean of the lifetime will be less than 270
minutes?
A.0.9987
B.0.0013
C.0.4987
D.0.3821

The lifetime of a certain battery follows a normal distribution
with a mean 276 minutes and standard deviation 25 minutes. We took
a random sample of 100 of these batteries. What is the probability
that the sample mean of the lifetime will be less than 270
minutes?

The weight of a type of dog follows Normal distribution with
mean of 44 pounds and standard deviation of 3 pounds.
1. What is the probability a dog of this type will weigh more
than 100 pounds? (Show your work.)
2. What is the probability a dog of this type will weigh more
than 10 pounds? (Show your work.)

Assume that the distribution of the weights for a brand of mints
is normal with mean 21grams and standard deviation 0.5 grams. Let X
be the weight of a randomly chosen mint from this brand.
a. Find the probability that a randomly chosen mint from this
brand weighs at least 20 grams.
b. If a mint has a weight more than 20% of all the mints in this
brand. Find the weight of this mint.
c. If a SRS of...

battery life follows a normal continuous probability
distribution with a population mean = 300 hours and a population
standard deviation of 30 hours. What is probability that a battery
tested will last for less than 270 hours?
What is probability that a battery tested will last between 270
and 330 hours?
The weakest 10% of the population will not exceed what battery
life?

The weight of lobsters caught in the ocean follows a normal
distribution with a mean of 1440 grams and a standard deviation of
2h grams.
(a) Given the probability that a lobster caught at random has a
weight of not more than 1530 grams is 0.9463. Calculate the value
of h and correct the answer to 2 decimal places.
(b) By using the value of h from (a), if 1250 lobsters
have a weight between 1350 and 1500 grams, estimate...

The inside diameter of certain type piston ring follows normal
distribution with mean 9.3 cm, and standard deviation 0.06 cm. A
sample of size 12 is selected from these pistons, and suppose
[(x)] denotes the sample mean.
1. What is the expected value of [(x)]? Answer to
1 decimal place.
2. What is the standard deviation of [(x)]? Answer
to 3 decimal places.
3. What is the probability that the sample mean [(x)]
will exceed 9.312 cm? Answer to 4...

(01.06 LC)
The weight of laboratory grasshoppers follows a Normal
distribution, with a mean of 90 grams and a standard deviation of 2
grams. What percentage of the grasshoppers weigh between 86 grams
and 94 grams? (3 points)
99.7%
95%
68%
47.5%
34%

The distribution of weights of United States pennies is
approximately normal with a mean (m) of 2.5 grams and a standard
deviation (s) of 0.03 grams.
a. What is the probability that a randomly selected penny weighs
less than 2.4 grams?
b. Describe the sampling distribution of the mean weight of 9
randomly chosen pennies?
c. What is the probability that the mean weight of 9 randomly
chosen pennies is less than 2.49 grams?
d. Sketch the two distributions (population...

Weights (X) of men in a certain age group have a normal
distribution with mean μ = 190 pounds and standard
deviation σ = 20 pounds. Find each of the following
probabilities. (Round all answers to four decimal places.)
(a) P(X ≤ 220) = probability the weight of a
randomly selected man is less than or equal to 220 pounds.
(b) P(X ≤ 165) = probability the weight of a
randomly selected man is less than or equal to 165...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 10 minutes ago

asked 14 minutes ago

asked 16 minutes ago

asked 34 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago