Finding Z-Scores, Standard Deviation, Mean and X

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between 2.9 and 3.8? 

Assume that the salaries of elementary school teachers in the United States are normally distributed with a

mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that

he or she makes more than $36,000.

Compute the probability P(X > 92).

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹ s IQ score is found to be 110. Find the z- score corresponding to this value.

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a

certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given

week the airline will lose less than 20 suitcases?

Find the probability of z occurring in the indicated region.

Find the probability of z occurring in the indicated region.

Use z-scores and the standard normal table to find the proportion for the following scenario.

A set of HS student heights are normally distributed with a mean of 59 in and a standard deviation of 8 in. Brandon is a HS student with a height of 77 in. What proportion of student heights are LOWER than Brandon's height?

Drag and drop the answers to show your work below.

z₇₇ = (​ (a)   - ​ (b)   ) / ​ (c)   = ​ (d)  

Answer from Z-Table: ​ (e)  

Use z-scores and the standard normal table to find the proportion for the following scenario.

A set of mathematics exam scores are normally distributed with a mean of 80.5 points and a standard deviation of 3 points. What proportion of exam scores are BETWEEN 81 and 86 points?

Drag & drop the correct answers to your work below. *Round z-scores to the nearest HUNDREDTH

z₈₁ = ​ (a)  

z₈₆ = ​ (b)  

Answer: ​ (c)   - ​ (d)   = ​ (e)  

A study examined a random sample of 60 residents and found the mean weight to be 145 pounds with a standard deviation of 32 pounds. At the 95% confidence level, use the normal distribution/empirical rule to estimate the MARGIN OF ERROR for the mean. *Round to the nearest TENTH

(a)