Stats Study Guide
The mean incubation time of fertilized eggs is 22 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (A)The 19th percentile for incubation times is ____ days? (round to the nearest whole number as needed (B)The incubation times that make up the middle 39% are ___ to ___ days? (round to nearest whole number, use ascending order) 2. As reported by a recent survey, the mean height of females 20 to 29 years old is 63.
6 inches. If the height is approximately normally distributed with a standard deviation of 2. inches, (A)What is the percentile rank of a 20-29 year old female who is 59. 8 inches tall? ___th percentile. (round to the nearest integer) (B)What is the percentile rank of a 20-29 year old female who is 70 inches tall? ___th percentile (C)What proportion of 20-29 year old females are between 59. 8 and 70 inches tall? (round to 4 decimal places as needed)
3.
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with the mean of 247 days and standard deviation of 20 days. A)What is the probability that a randomly selected pregnancy lasts less than 241 days? (round to 4 decimal places) (B)What is the probability that a random sample of 29 pregnancies has a mean gestation period of 241 days or less? (C)What is the probability that a random sample of 69 pregnancies has a mean gestation period of 241 days or less 4. A certain flight arrives on time 69% of the time. Suppose 199 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability.
A)What is the probability that exactly 121 flights are on time? (round to 4 decimal places) (B)What is the probability that at least 121 flights are on time? (C)What is the probability that fewer than 138 flights are on time? (D)What is the probability that between 138 and 148, inclusive, are on time? 5. The mean gas mileage for a hybrid car is 57 miles per gallon.
Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3. 5 miles per gallon. (A)What is the proportion of hybrids that gets over 62 miles per gallon? round to 4 decimal places) (B)What is the proportion of hybrids that gets 52 miles per gallon or less? (C)What is the proportion of hybrids that gets between 57 and 61 miles per gallon? (D)What is the probability that a randomly selected hybrid gets less than 46 miles per gallon? 6. In studies for a medication, 2% of patients gained weight as a side effect.
Suppose 592 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability.
(A)What is the probability that exactly 1 patient will gain weight as a side effect? round to 4 decimal places) (B)What is the probability that 1 or fewer patients will gain weight? (C)What is the probability that 2 or more patients will gain weight? (D)What is the probability that between 1 and 5, inclusive, will gain weight? 7. Suppose a simple random sample of size n=50 is obtained from a population whose size is N=15,000 and whose population with a specified characteristic is p= . 6 (A)Determine the mean of the sampling distribution of p. (round to 4 decimal places) (B)What is the probability of obtaining x = 32 or more individuals with the characteristic?
That is, what is P(p < or equal to .
54) (round to 4 decimal places) 8. Suppose a geyser has a mean time between eruptions of 73 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 24 minutes, (A)What is the probability that a randomly selected time interval between eruptions is longer than 84 minutes? (round to 4 decimal places) (B)What is the probability that a random sample of 9 time intervals between eruptions has a mean longer than 84 minutes? C)What is the probability that a random sample of 29 time intervals between eruptions has a mean longer than 84 minutes? 9. The number of chocolate chips in an 18 ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (A)What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (round to 4 decimal places) (B)What is the probability that a randomly selected bag contains fewer than 1100 chips? (C)What proportion of bags contains more than 1200 chips?
