Question

In: Statistics and Probability

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 5.8-in and a standard deviation of 1.1-in.

In what range would you expect to find the middle 68% of most head breadths?

Between ______ and _____.

If you were to draw samples of size 39 from this population, in what range would you expect to find the middle 68% of most averages for the breadths of male heads in the sample?

Between ____ and ______.

Solutions

Expert Solution

Solution:-

Given that,

a) mean = = 5.8

standard deviation = = 1.1

Using standard normal table,

P( -z < Z < z) = 68%

= P(Z < z) - P(Z <-z ) = 0. 68

= 2P(Z < z) - 1 = 0. 68

= 2P(Z < z) = 1 + 0. 68

= P(Z < z) = 1. 68 / 2

= P(Z < z) = 0.84

= P(Z < 0.99 ) = 0.84

= z  ± 0.99

Using z-score formula,

x = z * +

x = - 0.99 * 1.1 + 5.8

x = 4.7

x = z * +

x = 0.99 * 1.1 + 5.8

x = 6.9

Between 4.7 and 6.9

b) n = 39

=   = 5.8

= / n = 1.1 / 39 = 0.18

Using z-score formula  

= z * +

= -0.99 * 0.18 + 5.8

= 5.6

Using z-score formula  

= z * +

= 0.99 * 0.18 +5.8

= 6.0

Between 5.6  and 6.0


Related Solutions

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 5.9-in and a standard deviation of 0.8-in. In what range would you expect to find the middle 68% of most head breadths? Between______and ______. If you were to draw samples of size 50 from this population, in what range would you expect to find the middle 68%...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.1-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.3% or largest 2.3%. What is the minimum head breadth that will fit the clientele? min =...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.7-in and a standard deviation of 0.8-in. In what range would you expect to find the middle 98% of most head breadths? Between ___ and ___ . If you were to draw samples of size 34 from this population, in what range would you expect to find...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 7.1-in and a standard deviation of 0.9-in. In what range would you expect to find the middle 98% of most head breadths? Between ___ and _____. If you were to draw samples of size 37 from this population, in what range would you expect to find the...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 7.1-in and a standard deviation of 0.9-in. In what range would you expect to find the middle 98% of most head breadths? Between ___ and _____. If you were to draw samples of size 37 from this population, in what range would you expect to find the...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.5-in and a standard deviation of 1.1-in. In what range would you expect to find the middle 95% of most head breadths? Between ___ and ____ . If you were to draw samples of size 35 from this population, in what range would you expect to find...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.9-in and a standard deviation of 1.1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 2.5% or largest 2.5%. What is the minimum head breadth that will fit the clientele? min =...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.1-in and a standard deviation of 1.1-in. In what range would you expect to find the middle 95% of most head breadths? Between  and . If you were to draw samples of size 46 from this population, in what range would you expect to find the middle 95%...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6-in and a standard deviation of 1.2-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.9% or largest 1.9%. a) What is the minimum head breadth that will fit the clientele?             min...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined...
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 5.9-in and a standard deviation of 0.8-in. In what range would you expect to find the middle 50% of most head breadths? Between and . If you were to draw samples of size 41 from this population, in what range would you expect to find the middle...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT