Statistics 3 1. The empirical rule states that for a normal distribution: I Approximately _% of the data lies within 1 standard deviation from the mean i.\" :I; 10'] I Approximately _% of the data lies within 2 standard deviations from the mean (it i 20'} I Approximately _% of the data lies within 3 standard deviations from the mean (it 1 Bo} 2. Write the correct symbol for each of the following: a) Standard deviation of a sample h) Mean of a population c) Mean of a sample d) Standard deviation of a population 3. Label the following normal distribution to show the empirical role. Include the following: i\" 1 F + or p 1.1 it + 2:: it 2o it + 3a a So 6.8% 95% 99.1% 34% 13.5% 2.35% {i15% 4. According to the empirical rule, approximater what percent of area under the curve lies: a) To the left of it? d) Between [.1 +2o and n+3o'? b) To the right of pi 20'? e) Between 11 - o and p. + 20? c) To the left of ,u a? f} To the right of [1+3G'? 5. Costs for standard veterinary services at a local animal hospital follow a normal distribution with a mean of $80 and a standard distribution of $20. a. Label the values on the bottom of the normal curve below. X -30 -20 -10 10 20 30 b. What is the probability that the cost of the service is between $60 and $100? c. What is the probability that the cost of the service is between $40 and $120? d. What is the probability that the cost of the service is less than $407 e . What is the probability that the cost of the service is greater than $80? 6. Light bulbs are measured in lumens (light output), watts (energy used), and hours (life). A soft white light bulb has a mean life of 700 hours and a standard deviation of 35 hours. a) Assuming a normal distribution, what is the probability that a randomly selected soft white light bulb lasts 770 hours or more? b) The life of a soft white light bulb is considered to be below average in length if it lasts hours or less, and above average if it lasts hours or more. c) What is the probability of randomly selecting a soft white light bulb that lasts between 630 and 805 hours?For problems 7-10, draw and label normal distribution curves and answer the questions. 7. . The weights of the 50 football players are a) What percent of the players weigh between normally distributed with a mean of 178 pounds 178 lbs and 194 lbs? and a standard deviation of 8 pounds. b) What is the probability that a player weighs at most 170 lbs? c) What is the probability that a player weighs less than 162 lbs or greater than 194 Ibs? d) How many players weigh between 170 lbs and 186 lbs? 8. . A set of 120 test scores are normally distributed a) What percent of the scores are between 72 with a mean of 82 and a standard deviation of and 87? 5 . b) What is the probability that a score is greater than 77? c) What is the probability that a score is less than B2 or greater than 92? d) About how many students scored outside two standard deviations of the mean?9 . The pn'ce of a gallon of regular gasoline at ?'5 a] Wl'ICli' percent of gas stations sell a gallon of gas stations across the state is normally regular gas for less than $1.??? distn'buted with a mean of $21.15 and a standard deviation of 4-92. h] Wl'ICli' percent of gas stations sell a gallon of regular gas for at least $2.] I"? c} What is the probability that a gas station sells a gallon of regular gas for less than $1 .9? or greater than $2.05? d] About how many stations sell a gallon of regular gas for no more than $2.01 ? ID. . l'vtrs. Fuller recentty tested her 120 keyboarding a] About how many students can type at least 39 students to see how many words per minute words per minute? they can type. The results were normally distributed with a mean of 45 and a standard deviation of 6. In] About how many students can type within one standard deviation of the mean? c] Students need to be in the top 2% in order to be eligible for the national typing competition. If Carla can type 56 wpm, is she eligible? 11. The number of hours that the employees at the grooery store worked last week is normally distributed with a mean of 24 and a standard deviation of E. If there are t] total employees, approximately how many worked at least 3|] hours last week? 12. The grade point average {GPA} of the students at Lakeview High School is normally distributed with a mean of 3.1 and a standard deviation of I13. If there are 1801:) students enrolled at the school, approximately how many have a GPA between 2.5 and 33