Chapter 7 statistics solutions

1) Determine the area under the standard normal curve that lies to the left of ​(a)Z=1.31 (b)Z=1.06​ (c)Z=0.57​ and ​(d)Z=0.14.

2) Determine the area under the standard normal curve that lies to the right of (a)Z=0.64 (b)Z=-1.78 (c)Z=0.93 and (d)Z=0.59

3) Determine the area under the standard normal curve that lies between (a)Z=-0.64 and Z=0.64, (b)Z=-2.38 and Z=0, and (c) Z=-0.65 and Z=1.23

4) Find the​ Z-score such that the area under the standard normal curve to the right is 0.15

5) Find the​ z-scores that separate the middle 95​% of the distribution from the area in the tails of the standard normal distribution.

6) Find the value of zα α=0.18

7) Assume the random variable X is normally distributed with mean μ=50 and standard deviation

σ=77 Find the 97th percentile.

8) The mean incubation time for a type of fertilized egg kept at 100.33​°F is 22 days. Suppose that the incubation times are approximately normally distributed with a standard deviation of 2 days.

(a)What is the probability that a randomly selected fertilized egg hatches in less than

20 days?

(b) What is the probability that a randomly selected fertilized egg takes over

24 days to​ hatch?

(c) ) What is the probability that a randomly selected fertilized egg hatches between

18 and 22 days?

(d) Would it be unusual for an egg to hatch in less than

19 days? Why?

9) Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 56hours and a standard deviation of 3.3hours. With this​ information, answer the following questions.

(a) What proportion of light bulbs will last more than 62​hours?

​(b) What proportion of light bulbs will last 50 hours or​ less?

(c) What proportion of light bulbs will last between 58 and 62 hours?

​(d) What is the probability that a randomly selected light bulb lasts less than 45 hours?

10) The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

(a) Determine the 28th percentile for the number of chocolate chips in a bag.

(b) Determine the number of chocolate chips in a bag that make up the middle 96% of bags.

11) The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal​ distribution, with a mean of 19 minutes and a standard deviation of 2.5 minutes.

(a) The automotive center guarantees customers that the service will take no longer than

20minutes. If it does take​ longer, the customer will receive the service for​ half-price. What percent of customers receive the service for​ half-price?