Question

# A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.8...

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.8 years, and standard deviation of 2.9 years. If 5 items are picked at random, 2% of the time their mean life will be less than how many years?

Let X be a mean life span of the items in years.

We want to find the 2% of the time their mean life will be less than C years.

P(X < C) = 0.02

The below 2% of the time their mean life is below C years.

We will solve this problem by standardising.

P(X < C) = P ((X - µ)/σ < (C – 12.8)/2.9) = P(Z < (C – 12.8)/2.9)

P(Z < (C – 12.8)/2.9) = 0.02

The Z score to corresponding area is 0.02 is -2.05(using statistical table).

NORM.S.INV(0.02) = -2.05375 ………….. (Using Excel fuction)

(C – 12.8)/2.9= -2.05

C = -2.05*2.9 + 12.8

C = 6.855

If 5 items are picked at random, 2% of the time their mean life will be less than approximate 7 many years.

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• What is your marginal rate of consumption (MPC)? If your income increased \$1,000 per month until...
asked 1 minute ago
• Gender Bias in the Executive Suite Worldwide The Grant Thornton International Business Report (IBR) has described...
asked 2 minutes ago
• See the multivariate demand function below. Please show work so I can learn how this is...
asked 9 minutes ago
• Consider the map φ :Mnxn (R) → R defined by φ(M) = det(M), where det(M) is...
asked 9 minutes ago
• Use Excel to develop a regression model for the Hospital Database (using the “Excel Databases.xls” file...
asked 21 minutes ago
• A sample of ten people from an outer Sydney suburb travelled the following distances each day:-...
asked 24 minutes ago
• A horizontal spring with spring constant 2 N/m has one end connected to a wall while...
asked 31 minutes ago
• Lexington Company engaged in the following transactions during Year 1, its first year in operation: (Assume...
asked 33 minutes ago
• During the second half of 2014, the U.S. dollar made significant gains against all other major...
asked 37 minutes ago
• Pediatricians have been able to determine that the distribution of birth weights for boys is approximately...
asked 41 minutes ago
• Celebrity branding or celebrity endorsement is a marketing strategy used by organisations which involves celebrities using...
asked 41 minutes ago
• A manufacturing firm has set up a project for developing a new machine for one of...
asked 53 minutes ago