# Math Help - Normal and binomial distributions

1. ## Normal and binomial distributions

Hey everyone; I'm very new to this site but I am having such a hard time with my statistics class. My book is titled "elementary statistics" but it is a junior level course at my university. I have always maintained a high GPA and I am really starting to freak out in this class. Below are my question for this week (4 questions both with 2 parts) I know in the rule it said post different questions in different threads but I think this makes sense to keep them together. Any help would be appreciated.

1. The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of$45.

a. What is the probability that a randomly selected teacher earns more than $525 per week? (5 points) b. What is the probability a randomly selected teacher earns less than$435 per week? (5 points)

2. The introductory salaries for medical billing clerks are normally distributed with a mean of $24,800 and a standard deviation of$2850.

a. What percent of introductory salaries are less than $23,000? (5 points) b. What percent of introductory salaries are between$21,250 and $23,750? (5 points) 3. The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches. a. What is the probability that the mean annual snowfall during 40 randomly picked years will exceed 111.8 inches? (5 points) b. What is the probability that the mean annual snowfall during 40 randomly picked years will be between 105 inches and 112 inches? (5 points) 4. Merta claims that 74% of its trains are on time. a. Find the probability that among the 60 trains, 38 or fewer arrived on time. (5 points) b. Find the probability that among the 60 trains, 50 or more arrived on time. (5 points) 2. Originally Posted by rclements3 1. The weekly salaries of teachers in one state are normally distributed with a mean of$490 and a standard deviation of $45. a. What is the probability that a randomly selected teacher earns more than$525 per week? (5 points)
You need to convert these questions into z-scores. They are all quite similar.

$Z= \frac{X-\mu}{\sigma}$

$\mu = 490$
$\sigma = 45$
$x = 252$

$P(X>252) = P\left(Z>\frac{252-490}{45}\right) = \dots$

Normal distribution - Wikipedia, the free encyclopedia

Z table - Normal Distribution

3. Originally Posted by rclements3

4. Merta claims that 74% of its trains are on time.

a. Find the probability that among the 60 trains, 38 or fewer arrived on time. (5 points)

b. Find the probability that among the 60 trains, 50 or more arrived on time. (5 points)
You need to use a binomial distribution here.

$P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$

where where n = 60, p= 0.74, k<38