Answer questions show work

Question 1 (0.5 pts)

A psychology class consist of 14 students younger than 30 years old and 36 students 30-Year-old or older. If the professor selects names from the class list using random sampling, what is the probability that the first students selected will be 30 Years old or older?

Question 2 (0.5 pts each)

For each of the following Z-scores locations, determine whether the tail is on the right or the left side of the z-score locations:

1. Z= 3.00
2. Z= 0.75
3. Z= -1.38
4. Z= -.24
5. Z= -2.1

Question 3 (0.5 pts each)

For each of the Following Z-scores, find the proportion in the tail

1. Z= 2.20
2. Z= 1.60
3. Z= -1.50
4. Z= -0.70
5. Z=0.05

Question 4 (0.5 pts each)

Find each of the following probabilities for a normal distribution:

1. p(Z>0.25)
2. p(Z>0.75)
3. p(Z<1.20)
4. p(Z<-1.20)
5. p(Z>-0.75)

Question 5 (1 pts each)

Find each of the following probabilities for a normal distribution:

1. P(-0.25<Z<+0.25)
2. P(-0.90<Z<+0.90)
3. P(-1.50<Z<+1.50)
4. P(+0.25<Z<+1.1)
5. P(-0.75<Z<-0.25)

Question 6 (1 pts)

A population is normally distributed with a mean of µ= 45 and a standard deviation of ?= 3. What is the probability of randomly selecting a score that is greater than 43?

Question 7 (6 pts)

A test was given to children ages 7 to 10 to measure how long they can ride the bicycle without taking a break. The test shows that the children ages 7 to 10 can ride the bike for an average of µ=60 minutes without taking a break. Assuming that the distribution of the bike-riding times is normal with a standard deviation of ?=20 minutes, find each of the following proportions:

1. What proportion of children ride a bike for more than 90 minutes without taking a break?
2. What proportion of children ride a bike for less than 20 minutes without taking a break?
3. What proportion of children ride a bike for more than 30 minutes but less than 70 minutes without taking a break?