Question

1. A population is normally distributed with mean 19.1 and standard deviation 4.4. Find the probability that a sample of 9 values taken from this population will have a mean less than 22.
*Note: all z-scores must be rounded to the nearest hundredth.

2. A particular fruit's weights are normally distributed, with a mean of 377 grams and a standard deviation of 11 grams.
If you pick 2 fruit at random, what is the probability that their mean weight will be between 365 grams and 377 grams

3.The average GPA at a college is 3.19 with a standard deviation of 0.9.
If 34 students are selected at random, what is the probability that their average GPA will be between 3.23 and 3.71?

4. From 1985 to 2006, the average height of an NBA player was 6 foot 7 (79 inches). Suppose the distribution is approximately normal and the standard deviation is 0.5 inches. What is the probability that, of 34 NBA players selected at random, their average height is more than 79 inches?

5.IQ scores are normally distributed with a mean of 108 and standard deviation of 5. In a sample of 14 people, what is the probability that their average IQ score does not differ from the mean by more than two points?

6. Mathematics majors generally have one of the highest starting salaries. Suppose the average starting salary for mathematics majors is $52,000 with a standard deviation of $7,400. Find the probability that 26 mathematics majors have an average starting salary less than 54.

Answer 1

Solution:-
1. Given that mean = 19.1, standard deviation = 4.4 n = 9

P(X < 22) = P((X-mean)/sd/sqrt(n)) < (22-19.1)/(4.4/sqrt(9)))
= P(Z < 1.9773)
= 0.9761

2. Given that mean = 377, standard deviation = 11, n = 2

P(365 < X < 377) = P((365-377)/(11/sqrt(2)) < Z < (377-377)/(11/sqrt(2)))
= P(-1.5427 < Z < 0)
= 0.4382

3. Given that mean = 3.19, sd = 0.9, n = 34

P(3.23 < X < 3.71) = P((3.23-3.19)/(0.9/sqrt(34) < Z < (3.71-3.19)/(0.9/sqrt(34))
= P(0.2592 < Z < 3.3690)
= 0.3970

4. Given that mean = 79, sd = 0.5, n = 34

P(X > 79) = P(Z > 0) = 0.5