Question

a. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 45 months and a standard deviation of 3 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 48 and 51 months?b. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 64 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 64?c. A population of values has a normal distribution with μ=153 and σ= 39.5You intend to draw a random sample of size n=196Find P2, which is the score separating the bottom 2% scores from the top 98% scores. P2 (for single values) = Find P2, which is the mean separating the bottom 2% means from the top 98% means. P2 (for sample means) = Enter your answers as numbers accurate to 1 decimal place. round your answer to ONE digit after the decimal point! Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.d. A population of values has a normal distribution with μ= 117.8 and σ=73.1You intend to draw a random sample of size n=59Find the probability that a single randomly selected value is greater than 113. P(X > 113) = Find the probability that a sample of size n= 59 is randomly selected with a mean greater than 113. P(M > 113) = Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

a.

For this to make sense, we will plot the bell curve of the distribution.

It is general convention that:

65% of the values in the distribution lie between

`\begin{gathered} \bar{x}\pm\sigma \\ Where\colon \\ \bar{x}=\text{mean} \\ \sigma=s\tan dard\text{ deviation} \end{gathered}`
`\begin{gathered} 48\pm3=51\text{ or 45} \\ \text{This means that }65\text{ \% of the values lie within the range 45 and 51.} \\ Therefore,\text{ the range between 48 and 51 will be a half of 65\%} \\ (65)/(2)\text{ \% = 32.5\%} \end{gathered}`

35% is the percentage of cars that remain in service between 48 and 51 months

b.

We also plot the distribution curve as in a above,

`\begin{gathered} 64\pm7=71\text{ or }57 \\ \text{This means that }65\text{ \% of the values lie within the range 57 and 71.} \\ Therefore,\text{ the range between 57 and 64 will be a half of 65\%} \\ (65)/(2)\text{ \% = 32.5\%} \end{gathered}`

32.5% is the approximate percentage of lightbulb replacement requests numbering between 57 and 64