Question

This is a multi-part question.

First, find the following: For a standard normal distribution, find: P(-1.17 < z < 0.02)+__________

Second, resolve this: Assume that the readings at freezing on a
batch of thermometers are normally distributed with a mean of 0°C
and a standard deviation of 1.00°C. A single thermometer is
randomly selected and tested. Find the probability of obtaining a
reading less than -0.08°C.

P(Z<−0.08)= ____________

Third, resolve this: Assume that the readings at freezing on a
batch of thermometers are normally distributed with a mean of 0°C
and a standard deviation of 1.00°C. A single thermometer is
randomly selected and tested. Find the probability of obtaining a
reading between -0.798°C and 0.461°C.

P(−0.798<Z<0.461)= ______________

Last, resolve this: About ______% of the area under the curve of the standard normal distribution is between z=−0.279z and z=0.279 (or within 0.279 standard deviations of the mean).

Answer #1

P(-1.17<Z<0.02) can be calculated as

P(-1.17<Z<0.02) = P(Z<0.02) - P(Z<-1.17)

P-value can be find from Z table as follows

P(-1.17<Z<0.02) = P(Z<0.02) - P(Z<-1.17) = 0.5080 -
0.1210 = 0.387

Solution(b)

Given in the question

Mean = 0

Standard deviation = 1

We need to calculate

P(Z<-0.08), this can be calculated from Z table

P(Z<-0.08) = 0.4681

Solution(c)

P(-0.798<Z<0.461) = P(Z<0.461) - P(Z<-0.798) = 0.6776 -
0.2124 = 0.4652

Solution(d)

P(-0.279<Z<0.279) = P(Z<0.279) - P(Z<-0.279) = 0.6099 -
0.3901 = 0.2198

1. For a standard normal distribution,
find:
P(z > 2.32)
Keep four decimal places.
2. For a standard normal distribution,
find:
P(-0.9 < z < 0.95)
3. For a standard normal distribution,
given:
P(z < c) = 0.7622
Find c.
4. For a standard normal distribution,
find:
P(z > c) = 0.1753
Find c
5. Assume
that the readings at freezing on a batch of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C....

A. For a standard normal distribution, find:
P(-1.14 < z < -0.41)
B. For a standard normal distribution, given:
P(z < c) = 0.0278
Find c.
C. For a standard normal distribution, find:
P(z > c) = 0.4907
Find c.
D. Assume that z-scores are normally distributed with a mean
of 0 and a standard deviation of 1.
IfP(0<z<a)=0.4686P(0<z<a) = 0.4686
find a.
E. Assume that the readings at freezing on a bundle of
thermometers are normally distributed with a...

Assume that the readings at freezing on a batch of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C. A single thermometer is randomly selected and
tested.
Find the probability of obtaining a reading between -2.75°C and
0°C. P ( − 2.75 < Z < 0 ) =

3.Assume that the readings at freezing on a batch of
thermometers are normally distributed with a mean of 0°C and a
standard deviation of 1.00°C. A single thermometer is randomly
selected and tested. Find the probability of obtaining a reading
greater than 1.865°C. P(Z>1.865)=P(Z>1.865)= (Round to four
decimal places)
4.Assume that the readings at freezing on a batch of
thermometers are normally distributed with a mean of 0°C and a
standard deviation of 1.00°C. A single thermometer is randomly
selected...

Assume that the readings at freezing on a bundle of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C. A single thermometer is randomly selected and
tested. Find the probability of obtaining a reading less than
-1.503°C.
P(Z<−1.503)=P(Z<-1.503)=

Assume that the readings at freezing on a bundle of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C. A single thermometer is randomly selected and
tested. Find the probability of obtaining a reading between
-1.404°C and 2.955°C.
P(−1.404<Z<2.955)=

Assume that the readings at freezing on a bundle of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C. A single thermometer is randomly selected and
tested. Find the probability of obtaining a reading between 0.244°C
and 0.251°C.
P(0.244<Z<0.251)

Assume that the readings at freezing on a bundle of thermometers
are normally distributed with a mean of 0°C and a standard
deviation of 1.00°C. A single thermometer is randomly selected and
tested. Find the probability of obtaining a reading between
-0.276°C and 1.304°C.
P(−0.276<Z<1.304)=P(-0.276<Z<1.304)=

Assume that the readings at freezing on a batch of
thermometers are normally distributed with a mean of 0°C and a
standard deviation of 1.00°C. A single thermometer is randomly
selected and tested. Find the probability of obtaining a reading
between -2.95°C and 0.11°C.
Give your answer to 4 decimal places.

A.) Let XX represent the full height of a certain species of
tree. Assume that XX has a normal probability distribution with a
mean of 114.5 ft and a standard deviation of 7.8 ft.
A tree of this type grows in my backyard, and it stands 98.1 feet
tall. Find the probability that the height of a randomly selected
tree is as tall as mine or shorter.
P(X<98.1)P(X<98.1) =
My neighbor also has a tree of this type growing in...

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