Simple and Basic Statics Problems -
Problem 1 - Find the area under the normal curve that lies to the left of the following z values.
a. z = -1.30
b. z = -2.56
c. z = -3.20
d. z = -0.64
Problem 2 - Find the probability that a piece of data picked at random from a normal population will have a standard store (Z) that lies to the left of the following z values.
a. z = 2.10
b. z = 1.20
c. z = 3.26
d. z = 0.71
Problem 3 - Find the area under the standard normal curve to the right of z = -2.35, P(z > - 2.35).
Problem 4 - Find the following areas under the standard normal curve.
a. to the right of z = -0.47, P(z > -0.47)
b. to the right of z = -1.01, P(z > -1.01)
c. to the right of z = -3.39, P(z > -3.39)
Problem 5 - Find the area under the standard normal curve between -1.39 and the mean, P(-1.39 < z < 0.00).
Problem 6 - Find the following:
a. P(-3.05 < z < 0.00)
b. P(-2.43 < z < 1.37)
c. P(z < -2.17)
d. P(z > 2.43)
Problem 7 - a. Find the standard z-score such that 80% of the distribution is below (to the left of) this value.
b. Find the standard z-score such that the area to the right of this value is 0.15.
c. Find the two z-scores that bound the middle 50% of a normal distribution.
Problem 8 - Based on a survey conducted by Greenfield Online, 25-34-year-olds spend the most each week on fast food. The average weekly amount of $44 was reported in a May 2009 USA Today Snapshot. Assuming that weekly fast food expenditures are normally distributed with a standard deviation of $14.50, what is the probability that a 25- to 34-year-old will spend
a. less than $25 a week on fast food?
b. between $30 and $50 a week on fast food?
c. more than $75 a week on fast food?
Problem 9 - Depending on where you live and on the quality of the daycare, costs of daycare can range from $3,000 to $15,000 a year (or $250 to $1,250 monthly) for one child, according to BabyCenter. Daycare centers in large cities such as New York and San Francisco are notoriously expensive. Suppose that daycare costs are normally distributed with a mean equal to $9,000 and a standard deviation equal to $1,800.
a. What percentage of daycare centers will cost between $7,200 and $10,800 annually?
b. What percentage of daycare centers will cost between $5,400 and $12,600 annually?
c. What percentage of daycare centers will cost between $3,600 and $14,400 annually?
d. Compare the results from parts (a) through (c) with the empirical rule. Explain the relationship.
Problem 10 - According to ACT, results from 2008 ACT testing found that students had a mean reading score of 21.4 with a standard deviation of 6.0. Assuming that the scores are normally distributed,
a. Find the probability that a randomly selected student has a Reading ACT score less than 20.
b. Find the probability that a randomly selected student has a Reading ACT score between 18 and 24.
c. Find the probability that a randomly selected student has a Reading ACT score greater than 30.
d. Find the value of the 75th percentile for ACT scores.