A normal distribution has a mean of 32 and a standard deviation of 4. Find the probability that a randomly selected xx -value from the distribution is at most 35. Round to four decimal places.

Question
Probability
A normal distribution has a mean of 32 and a standard deviation of 4. Find the probability that a randomly selected xx -value from the distribution is at most 35. Round to four decimal places.

2021-02-04
To find the probability of a selected x-value being at most 35, you need to find the corresponding z-score and then use a z-score table. The area below the curve for the z-score is then the probability that the value will be at most 35.
To find the corresponding z-score, use the formula $$\displaystyle{z}=\frac{{{x}−μ}}{ Relevant Questions asked 2021-01-27 A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size \(\displaystyle{n}={153}$$ is drawn.
Find the probability that a single randomly selected value is between 188 and 206.6 round your answer to four decimal places.
P=?
A population of values has a normal distribution with mean =136.4 and standard deviation =30.2. A random sample of size $$\displaystyle{n}={158}$$ is drawn.
Find the probability that a sample of size $$\displaystyle{n}={158}$$ is randomly selected with a mean greater than 135. Round your answer to four decimal places.
$$\displaystyle{P}{\left({M}{>}{135}\right)}=$$?
A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size $$\displaystyle{n}={153}$$ is drawn.
Find the probability that a sample of size $$\displaystyle{n}={153}$$ is randomly selected with a mean between 188 and 206.6. Round your answer to four decimal places.
P=?
A population of values has a normal distribution with mean =136.4 and standard deviation =30.2. A random sample of size $$\displaystyle{n}={158}$$ is drawn.
Find the probability that a single randomly selected value is greater than 135. Roung your answer to four decimal places.
$$\displaystyle{P}{\left({X}{>}{135}\right)}=$$?
A population of values has a normal distribution with mean 18.6 and standard deviation 57. If a random sample of size $$\displaystyle{n}={25}$$ is selected,
Find the probability that a sample of size $$\displaystyle{n}={25}$$ is randomly selected with a mean greater than 17.5 round your answer to four decimal places.
P=?

Assume that the random variable Z follows standard normal distribution, calculate the following probabilities (Round to two decimal places)
a)$$P(z>1.9)$$
b)$$\displaystyle{P}{\left(−{2}\le{z}\le{1.2}\right)}$$
c)$$P(z\geq0.2)$$

A population of values has a normal distribution with mean = 37.4 and standard deviation 77.4. If a random sample of size $$\displaystyle{n}={15}$$ is selected,
Find the probability that a single randomly selected value is greater than 53.4. Round your answer to four decimals.
$$\displaystyle{P}{\left({X}{>}{53.4}\right)}=$$?
A distribution of values is normal with a mean of 166.1 and a standard deviation of 73.5.
Find the probability that a randomly selected value is between 151.4 and 283.7.
$$\displaystyle{P}{\left({151.4}{<}{X}{<}{283.7}\right)}=$$ Incorrect
$$\displaystyle{P}{\left({X}{<}{113.4}\right)}=$$?
A population of values has a normal distribution with $$\displaystyle\mu={77}$$ and $$\displaystyle\sigma={32.2}$$. You intend to draw a random sample of size $$\displaystyle{n}={15}$$
Find the probability that a sample of size $$\displaystyle{n}={15}$$ is randomly selected with a mean between 59.5 and 98.6. $$\displaystyle{P}{\left({59.5}{<}\overline{{{X}}}{<}{98.6}\right)}=$$?