Question

The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with mean μ and standard deviation σ = 2.4. A simple random sample of four plants of this variety is selected. The number of days until maturity for each plant is given below $\text{63 69 62 66}$

Based on these data, a 99% confidence interval for μ, in days, is

• 65.00 ± 3.09.

• 65.00 ± 2.35.

• 65.00 ± 4.07.

• 65.00 ± 1.55.

Answer 1

Ans: We use z* as multiplier when population satandard deviation is known.

$\sigma =2.4,n=4,\bar{x}=65$

z* for 90% confidence interval is 1.645

Confidence interval=

$\bar{x}\pm z^* \sigma/\sqrt{n}$

$=65\pm 1.645*2.4/\sqrt{4}$

$=65\pm 1.645*1.2$

$=65\pm 1.97$

$=(63.03,66.97)$

Hence,Option a is correct.